' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]LF L}BBL] X  ` 鷎귭෍ᷩ췩緈JJJJx Lȿ L8ᷭ緍췩 緍i 8 `巬 췌`x (`(8`I`B` ``>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)' `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y& 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪФ`+*xS&x'8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"ųųೳŪŪųųij  !"#$%&'()*+,-./0123456789:;<=>?   1 '" *"( (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0"):$(%"%:$(%"%$$2%4%$$2%4%$(2()!)E(!8b $!H(+ "@H !D)"E` @ $ C ` DQ &J80^݌Hh ü ü݌ ռ ռ ռA ļD ļ? ļAEDE?HJ>h Լ ռ ռ ռ`HJ>݌h Hh݌`葠葠ȔЖȔЖȠHIHHHHhHH݌hHhHh݌H6 VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`   LDcpq` [` ~  LӜu`".Q`pNФbptťܥm2<(-Py0\|e<6e<g< JJJJj귍hI  aUL@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭ͲLɍ [LLĦ__ ^ 9 LҦ3 9 a   0LjLY u< (_9 ˭ɠuɠK_9 ?LˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0h8` [L NС õ`A@` ŵL^Lõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmx- ( " Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈ۭm浍浭m䵍䵩m嵍`"L ŵ8ŵH ~(`# d ֠Ġz# u`0:7900m6E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN":V19:H1:NL4:5300:5500:78556C2;" / ";D2;" = ";C4:5300:V19:H1:NL4:5500:785565:3:3);:8:3:3);:MD1:M12:6@ADD/SUBTRACT THE EQUATIONS`7JMDA3A1:BCT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:78355RE$;" / ";D2;" = ";P2$(2):V19:H1:NL4:5300:5500:783558:22:" = ":19:1:C2;" / ";D2;" = ";:"";C2$:CH$C2$:6400:BADİ5500:78556(C2$)C4Ģ8:29((C4)):C4:5400:S6" = ";P2$(1):V19:H1:NL4:5300:5500:7805{419:1:COB2:VA$"Y":EX0:20000:RE$;" / ";D2;" = ";:"";C2$:C2$""78354C1$P2$(2):30000:CĢ8:18:COB4:VA$"Y":EX2:20000:RE$:S60:V19:H1:NL4:5500:7855@5E3E31::"SORRY, THAT IS INCORRE$"X":EX0:20000:RE$;" / ";D2;" = ";:"";C2$:C2$""78153C1$P2$(1):30000:CĢ8:17(C1$):C1$:S60:V19:H1:NL4:5500:78353E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7805,4RE$;" / ";D2;5300:5500:7775J2nC1;" / ";D1;" = ";C3:5300:V19:H1:NL4:5500:77752x4:3:3);:7:3:3);:D21Ģ8:3:5700:V8:H13:DAA2:DBB2:DCC2:25000:79002}5400:"DIVIDE #2 BY ";D2;": TERM BY TERM."25:3:5700:8:3:5700;319:1:COA2:VA2):V19:H1:NL4:5300:5500:7755v1_7:22:" = ":19:1:C1;" / ";D1;" = ";:"";C2$:CH$C2$:6400:BADİ5500:77751d(C2$)C3Ģ7:29((C3)):C3:5400:S60:78002iE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN":V19:H1:NL4:D1;" = ";:"";C2$:C2$""7755|0PC1$P1$(2):30000:CĢ7:18:COB3:VA$"Y":EX2:20000:RE$:S60:V19:H1:NL4:5500:77750UE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7755"1ZRE$;" / ";D1;" = ";P1$((C1$):C1$:S60:V19:H1:NL4:5500:7755/AE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7725/FRE$;" / ";D1;" = ";P1$(1):V19:H1:NL4:5300:5500:77250K19:1:COB1:VA$"Y":EX0:20000:RE$;" / ";D11Ģ7:3:5700:V7:H13:DAA1:DBB1:DCC1:25000:7800C.(S60s.-5400:"DIVIDE #1 BY ";D1;": TERM BY TERM.".24:3:5700:7:3:5700.719:1:COA1:VA$"X":EX0:20000:RE$;" / ";D1;" = ";:"";C2$:C2$""7735)/<C1$P1$(1):30000:CĢ7:170:S60:7600r-E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN":V19:H1:NL4:5300:5500:7555-MU(2);" * ";C2;" = ";C4:5300:V19:H1:NL4:5500:7555-5:3:3);:8:3:3);:MD1:M12:- ACTUALLY DO DIVISION-6300:.#T.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7535,~MU(2);" * ";RE$;" = ";P2$(2):V19:H1:NL4:5300:5500:7535,8:22:" = ":19:1:MU(2);" * ";C2;" = ";:"";C2$:CH$C2$:6400:BADİ5500:7555 -(C2$)C4Ģ8:29((C4)):C4:540";P2$(1):V19:H1:NL4:5300:5500:7505z+o19:1:COB2:VA$"Y":EX0:20000:MU(2);" * ";RE$;" = ";:"";C2$:C2$""7535+tC1$P2$(2):30000:CĢ8:18:COB4:VA$"Y":EX2:20000:RE$:S60:V19:H1:NL4:5500:7555?,yE3E31::"SORRY, THAT IS INCORREC:20000:MU(2);" * ";RE$;" = ";:"";C2$:C2$""7515*`C1$P2$(1):30000:CĢ8:17(C1$):C1$:S60:V19:H1:NL4:5500:7535*eE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7505(+jMU(2);" * ";RE$;" = 3MU(1);" * ";C1;" = ";C3:5300:V19:H1:NL4:5500:7460)L4:3:3);:7:3:3);:MU(2)1Ģ8:3:5700:V8:H13:DAA2:DBB2:DCC2:25000:7600)Q5400:"MULTIPLY #2 BY "MU(2)": TERM BY TERM.")V5:3:5700:8:3:57004*[19:1:COA2:VA$"X":EX0:5500:7440c($7:22:" = ":19:1:MU(1);" * ";C1;" = ";:"";C2$:CH$C2$:6400:BADİ5500:7460()(C2$)C3Ģ7:29((C3)):C3:5400:S60:7500(.E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN":V19:H1:NL4:5300:5500:7460:)7440c'C1$P1$(2):30000:CĢ7:18:COB3:VA$"Y":EX2:20000:RE$:S60:V19:H1:NL4:5500:7460'E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7440 (MU(1);" * ";RE$;" = ";P1$(2):V19:H1:NL4:53005500:7440q&E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7415& MU(1);" * ";RE$;" = ";P1$(1):V19:H1:NL4:5300:5500:7415'19:1:COB1:VA$"Y":EX0:20000:MU(1);" * ";RE$;" = ";:"";C2$:C2$""B1:DCC1:25000:7500%S60Q%5400:"MULTIPLY #1 BY "MU(1)": TERM BY TERM."m%4:3:5700:7:3:5700%19:1:COA1:VA$"X":EX0:20000:MU(1);" * ";RE$;" = ";:"";C2$:C2$""7420 &C1$P1$(1):30000:CĢ7:17(C1$):C1$:S60:V19:H1:NL4:$A3A1D1:B3B1D1:C3C1D1>$A4A2D2:B4B2D2:C4C2D2o$(A3)(A4)(B3)(B4)ER11:5950:7245$D11D21ER13:5950:V4:H1:NL2:5500:$7700$ ACTUALLY DO MULTIPLICATION$6300%MU(1)1Ģ7:3:5700:V7:H13:DAA1:DB:5800:D2(G$):D21G$""N#G$""V5:H13:DAA2:DBB2:DCC2:25000:7350j#D20ER10:5950:7305#G2D2(G2D2)ER9:5950:7305#5:12:"(";:V5:H13:DAA2:DBB2:DCC2:25000:" ) / ";D2#5:3:3);:5400:D10D11$D20D217300 "\D10ER10:5950:7250F"aG1D1(G1D1)ER9:5950:7250"f4:12:"(";:V4:H13:DAA1:DBB1:DCC1:25000:" ) / ";D1"p5400"4:3:3);:5:3:5700#5400:17:1:R3$"2 "R2$::"HIT ";::"RETURN";::" FOR NO CHANGE.":V17:H35(B2T2))OK1-!JT2,T1:OKER12:5950:h!MR3$"DIVIDE EQUATION #":V4:H1:NL2:5500:4:3:5700!R17:1:R3$"1 "R2$::"HIT ";::"RETURN";::" FOR NO CHANGE.":V17:H35:5800:D1(G$):D11G$"""WG$""V4:H13:DAA1:DBB1:DCC1:25000:G11:G21P /ZZ25:(A1ZZ)(A1ZZ)(B1ZZ)(B1ZZ)(C1ZZ)(C1ZZ)G1ZZX 0ZZ 4ZZ25:(A2ZZ)A2ZZ(B2ZZ)B2ZZ(C2ZZ)C2ZZG2ZZ >ZZ C5400!HOK0:T11G1:T21G2:G1T1(G1T1)G2T2(G2T2)((A1T1)(A2T2)(B1T1)B3MU(1)B1:C3MU(1)C1?A4MU(2)A2:B4MU(2)B2:C4MU(2)C2o(A3)(A4)(B3)(B4)ER4:5950:7018MU(1)1MU(2)1ER13:5950:V4:H1:NL2:5500:7400  DIVISION OF EQUATION BY A CONSTANT)FIND GCF OF THE 3 COEFFICIENTS *$)64(MU$)487045cS40:MU(2)0MU(2)1V5:H13:DAA2:DBB2:DCC2:25000:S41:MU(2)1:7100|V5:H12((MU(2)))V:H:MU(2);"(";:H13:DAA2:DBB2:DCC2:25000:" )"5:3:" "5400MU(1)0MU(1)1MU(1)1A3MU(1)A1:17:H37:5800:MU(2)(G$):MU(2)1G$""DS30:MU$G$:IN1S31Y(G$)0MU$G1${S11(MU$)13MU(2)1:7057S11S31MU(2)1ER6:5950:7050S11MU(2)1ER5:5950:V4:H1:NL2:5500:MU$"0"ER3:5950:7045(MUsMU(1)0MU(1)1V4:H13:DAA1:DBB1:DCC1:25000:MU(1)1:7045[uV4:H12((MU(1)))vV:H:MU(1);"(";:H13:DAA1:DBB1:DCC1:25000:" )"5400:4:3:" ":5:3:5700(17:1:R1$"2 "R2$::"HIT ";::"RETURN";::" FOR NO CHANGE.":V::"RETURN";::" FOR NO CHANGE.":V17:H37:5800:MU(1)(G$):MU(1)1G$""imS30:MU$G$:IN1S31~n(G$)0MU$G1$oS11(MU$)13MU(1)1:7027pS11MU(1)1ER5:5950:qMU$"0"ER3:5950:7010r(MU$)64(MU$)487010BZZ$" "BAD1ZZ:PX SUBR IF STUDENT ENTERS CORRECT VALUE ON MAIN MENUm]5400:IN7010,8000,9000b5050:R1$"MULTIPLY EQUATION #":R2$"BY WHAT VALUE?"gG327200j5400:V4:H1:NL2:5500:4:3:5700Ml17:1:R1$"1 "R2$::"HIT ";000:P1$(1)RE$2VA$"Y":COB3:20000:P1$(2)RE$VVA$"X":COA4:20000:P2$(1)RE$zVA$"Y":COB4:20000:P2$(2)RE$CHECK FOR NON-NUMERICCHARACTERS IN CH$. BAD0:ZZ1(CH$):ZZ$(CH$,ZZ,1):(ZZ$"0"ZZ$"9")ZZ$"+"ZZ$"-" SUBR TO PRINT ERROR MESSAGE9HM11M12E1E11:5980ERE2E21\5400:(ER$(ER))120āZZ0((ER$(ER))40.01):(ER$(ER),140ZZ,40):ZZ:5990aER$(ER)f5300:5400: SUBR TO PUT CORRECT ANSWERS TO MULTVA$"X":COA3:EX0:20W AR$N:AR$::+ SUBR GET ROUTINE<G$"":G1$""FV:HG1$:G1$(13)G1$"."G1$(8)G$G$G1$:H:V:G$;:5830G1$"."5830G1$(13)ıG$""ĺG1$;" ";G1$;(G$)1G$(G$,(G$)1):5830G$"":5830>:34,0:35,24:L SUBR ERROR MESSAGES FOR INCORRECT CHOICE ON MAIN MENU[ER0:5400f17:1M11(IN2IN3)ER1:5950:M12IN3ER2:5950:M12IN1MDER7:5950:M13IN3ER16:5950:D SUBR PRINT REVERSE ARROBOTTOM OF SCREENR16368,0:24:8:"PRESS ";::"RETURN";::" TO CONTINUE. ";l(16384)141ī532016368,0:24:7:30);: SUBR TO ERASE MAIN MENU"34,16:19::34,0:|ERASE DIFF PARTS OF THE SCREEN34,V1:35,VNL1:V:QUATIONS":2("3) SOLVE FOR VARIABLE 'X' OR 'Y'84n717:1:"ENTER ONE OF THE FOLLOWING:";::" ";IN$|8IN(IN$)<IN1IN35105FP SUBR TO PRINT LINE ACROSS SCREENZV:1dZZ139:"-";:ZZn SUBR FOR "HIT RETURN-A CONSTANT"::"2) DIVIDE EQUATION(S) BY A CONSTANT"cV17:H29:5800:G3(G$):G31G325055i SUBR TO PRINT MAIN MENU5400 19:1"1) MULTIPLY/DIVIDE ";::1;::" OR ";::2;::" BY A CONSTANT": "2) ADD OR SUBTRACT E2:"WE'RE ALL DONE NOW, ";N$;"."S12:3:"THANK YOU FOR SPENDING TIME WITH ME."y14:10:"I HOPE YOU ENJOYED IT."22: SUBR FOR DECISION ON MULT OR DIV5400:G304:"ENTER ONE OF THE FOLLOWING:":::"1) MULTIPLY EQUATION(S) BY ------":;"ELIMINATING A VARIABLE ........ ";TE(1):k"SOLVING LINEAR EQUATIONS ...... ";TE(2):"COMPUTATIONAL ERRORS .......... ";TE(3)31);"---"::"GRAND TOTAL ................... ";TE(1)TE(2)TE(3)5300 :10:10(N$) NEXT PROBLEM, ";::"Q";::" TO QUIT.";f16384,128:ZZ(16384)128:16368,0:ZZ81ZZ113700vZZ13660200:NEXT PROBLEM:11:"TOTAL ERROR ANALYSIS"::::" ERROR NUMBER" " ----- AL ERRORS .......... ";E3Xq31);"---"::"TOTAL ......................... ";E1E2E3v19:ME$(3((E1E2E30)(E1E2E31))(3(1)))TE(1)TE(1)E1:TE(2)TE(2)E2:TE(3)TE(3)E3:ZZ(0):P%N%İ5300:700)24:"HIT ";::"RETURN";::" FOR:520"GRAPH"fX:7:"ERROR ANALYSIS FOR PROBLEM #";P%::::" ERROR NUMBER"]" ----- ------":b"ELIMINATING A VARIABLE ........ ";E1:g"SOLVING LINEAR EQUATIONS ...... ";E2:l"COMPUTATION::".":CH2:5300:45000t :5400:"SINCE THE SOLUTION CHECKS IN BOTH"::"EQUATIONS, WE KNOW IT'S CORRECT.":5300 D5400:"WE CAN ALSO CHECK THE SOLUTION BY"::"GRAPHING THE EQUATIONS.":24:12:"ONE MOMENT, PLEASE.";:22::(4);"BLOAD CHAIN, A520"25000 V3:5200# V16:52002 ER0:5100D 5600:ER500S ER0:7000e FOUND2500 &5400:"NOW, I'LL CHECK YOUR ANSWER. FIRST,"::"I'LL CHECK EQUATION ";::1;::".":CH1:5300:45000 05400:"NEXT, I'LL CHECK EQUATION ";::2;)(B2)S11:M12A `A1B1A2B2320: EQUATIONS ARE PARALLELZ cR10:XR(R):YR(R)k eX0Y0355 hC1A1XB1Y:C2A2XB2Y |::"SOLVE": 1:7::"1" 2:7:"2": V1:H13:DAA1:DBB1:DCC1:25000:V2:H13:DAA2:DBB2:DCC2:ER$(20),ME$(8):10000# AR$"-->"7 DO N% PROBLEMSC P%P%1V E10:E20:E30j , SETUP PROBLEMs 6R10 @A1R(R):A10320 JA2R(R):A20330 TB1R(R):B10340 YB2R(R):B20345 \M11:MD0:FOUND0 ^S10:(A1)(A2)(B1ITLE PAGE P51000:GET NAME7 Z55000:INSTRUCTIONS d:13:"ENTER THE NUMBER AND HIT RETURN.":10:"HOW MANY PROBLEMS (1 TO 9)? ";NU$ n(NU$)2100 x(NU$)((NU$))(NU$)1(NU$)9100 N%(NU$):P%0 R(X)((1)X1)X2 w33,40:34,0, SOLVING SIMULTANEOUSD LINEAR EQUATIONS U VERSION 1.0m COPYRIGHT (C) 1983MICROCOMPUTER WORKSHOPS PORTCHESTER, NY2RC%600<ZZ0:ZZ$"":Z$"":Z1$"":C1$"":C2$"":CO0:CH$"":VA$"":RE$"" F50000:T                                      );" / ";CH;")"YtRZM5:5400:CO(1);" / ";CH;" = ";:900:C2$G$:CH$C2$:6400:BAD44370tW(C2$)(CO(1)CH.5)E3E31::"THAT IS INCORRECT."::CO(1);" / ";CH;" = ";(CO(1)CH.5):5300:44370t\OP$" + ":CO(1)CH0OP$" - "HufVS2:1:18E31::"THAT IS INCORRECT."::LT$;" / ";CH;" = ";C1$:5300:44310rs VS2:CO(1)0Ė6:16(C1$));C1$:44400s4(C1$)((CO(1)))((CH))6Ė1:12(C1$)((CO(1)))((CH)));:44360s>6:8(C1$)((CO(1)))((CH)));tHC1$;" + (";CO(12);" / ";CH*r䬢VS:3:3):VS2:3:5700r 5400:"NOW YOU MUST SIMPLIFY BY PERFORMING THE"::"DIVISION ON EACH SIDE.":5300rZM5:5400:LT$;" / ";CH;" = ";:900:C2$G$:C2$""44310DsT1CO:CO(COCH.5):EX0:20000:C1$RE$:COT1:30000:CE3T, ";CO;".":5300:44000+qCO(1)044250qVSVS2:VS2:1:13(LT$)(((CO(1))))((CH)));"(";LT$;1);:CO(1)0ĺ"+";:44230q"-";qƬ1);(CO(1));") / ";CH;" = ";CO(2);" / ";CH:44300 rڬVS2:19(LT$)((CH)):LT$;" / ";CH;" = ";CO($(21))40):5300:44000pD(CO(1)0CHCO)(CO(1)0(COCH(COCH)).00001(CO(1)CH(CO(1)CH)).00001(CO(2)CH(CO(2)CH)).00001)44200pNCO(1)0ER9:5950:qX5400:E2E21:"TO SOLVE FOR ";VA$;", YOU MUST DIVIDE BY"::"ITS COEFFICIENoZM5:5400:"DIVIDE BOTH SIDES BY WHAT VALUE: ";:900:G$""44000:CH$G$:CH$"1"CH$"+1"CH1:44020o嫰6400:BAD44120oCH(CH$):CH0ĭCH$"0"CH$"-0"CH$"+0"ER10:5950:44000o﫭CH044120pCH1İ5400:(ER$(21),40):(ER$(21),(ERpn(C2$)(CO(2)NUDE.5)E3E31::"THAT IS INCORRECT."::CH$;CO(2);" = ";(CO(2)NUDE.5):5300:43400nVS2:25:(CO(2)NUDE.5);14(((CO(2)NUDE.5))))nCO(CONUDE.5):CO(1)(CO(1)NUDE.5):CO(2)(CO(2)NUDE.5):VSVS2:jNCORRECT."::CH$;CO(1);" = ";(CO(1)NUDE.5):5300:43370cmtOP$" + ":CO(1)NUDE0OP$" - "m~VS2:1:18(C1$)((((CO(1)NUDE.5)))));C1$;OP$;((CO(1)NUDE.5)):VS2:3:5700mZM5:5400:CH$;CO(2);" = ";:900:C2$G$:C2$""43400(C1$)(CH$)((CO(1)))10Ė1:16(C1$)(CH$)((CO(1))));:43360olV6:11(C1$)(CH$)((CO(1))));l`C1$;" + ";OP$;CH$;CO(1);CL$ljZM5:5400:CH$;CO(1);" = ";:900:C2$G$:C2$""43370: ";:G$""3G$:G$"0"1300:G$;{10:16:"0";:400:1:18:"5Y + -Y = ":24:13:"TYPE 4Y: ";:G$""(G$:G$"4"1320:G$;:G$""-G$:G$"Y"G$"y"1325:"Y";210:18:"+ 4Y";:400:1:18:"5 + -5 = "(8);(8);(8):P*U*U**U*U*(U*U*U  A  *@TP((*A*@ T U*U*U**U*U*U P*U*U*U@  A U"U U*P (P*U*U**U*U*UP*U*U*U**U *U P*UU*U*U**U*U*U P*U*U*UU**U*U*P*U*U*@*U*U**U*U* U*U*U  A  *@TP(DU*U*U**U*U*U @*U*U*UP  A E"Q (P*(D*A T  T*U*U**U*U*UP*U*U*U**U *U T*UU*U*U @*U T*U UP*@ P (PT(UU**U*U*P*U*U*@*U*U**U*U*T*U*U U T(A*E*U *@TP*(UDU*U*U**U*U*U @*U*U*UU A* E"Q (P*(UD*A T  T*U*U**U*U*U P*U*U*U**U @*UT*UU**U @*U T*U UT*A P (P(UU**U*U*P*U*U* U T*A*E*U *@PP*(UD U*U*U**U*U*U @*U*U*U U A* E"Q (P(UA U*U*U**U*U*U P*U*U*U**U P*U U*U*UU**U *U P*UUBTRACT, I WILL CHANGE THE SIGNS OF"::"THE TERMS IN THE SUBTRAHEND.":10034,9::8:12:"+";:15:"-X - Y = -5";:8:1:" ";:10:1 ::3:"NOW YOU MUST PERFORM THE ADDITION.":15:L$;:"ADD THE EQUATIONS TERM BY TERM."::"X + -X = ":24:U**U *U P*U U T*A T (P(UU**U*U*UP*U*U*U P*@*E*U @PP*(UD U*U*U**U*U*U @*U*U*U U A* E"Q P(UA U*U*U**U*U*U P*U*U*U**U*U*(U*U*UU**U *U P*U@ T(A T (P(U**U @*UP*U (*A*A T "U U*U*U**U*U*U *U*U*U  A  E*Q P("@ AU*U*U**U*U*U P*U*U*UU**U*U**U*U*UU*U*U @*U P*U@  A T" U*P(U**U @*UP*U (*A*A T "U T*U*U**U*U*U*U*U*U  A  E*Q P("@ AU*U*U**U*U*U P*U*U*U@*U*U**U*U*P*U*U U**U*U**U*U*U             200:24:13:"PRESS <2>: ";7G$:G$"2"1250:G$;34,15::16::"1) ADD THE EQUATIONS"::"2) SUBTRACT THE EQUATIONS":24:13:"PRESS <2>: ";G$:G$"2"1270:G$;K34,9::8::"-->";::12:"-";:9:11:"-----------------":::"TO S8);(8);(8):24:13:"PRESS <5>: ";:G$""EG$:G$"5"1220:G$;8:23:"= 5";:34,9:::" NOW THAT WE HAVE EQUALIZED THE"::"COEFFICIENTS OF X, OUR NEXT STEP IS TO"::"ADD OR SUBTRACT THE EQUATIONS.":1005:1:" ";:8:1:" ";::RM BY TERM."::"4X / 4 = ":24:13:"PRESS : ";:G$""]G$:G$"X"G$"x"1180:"X";8:16:"X";:400:18:1:"4Y / 4 = "(8):24:13:"PRESS : ";:G$""G$:G$"Y"G$"y"1205:"Y";*400:8:18:"+ Y";:18:1:"20 / 4 = "(0TI%5400:"NOW SIMPLIFY THE LEFT SIDE BY PERFORMING":"THE MULTIPLICATION.":5300I%ZM5:5400:CKV;" * ";KV;" = ";:900:C2$G$:CH$C2$:6400:BAD9710I%(C2$)CKVKVE3E31::"THAT IS INCORRECT."::CKV;" * ";KV;" = ";CKVKV:5300:97100J%CO00H%(KV)1(CKV)19720KH%COSA:VA$"X":KV$"X"VA$"("(X)")"H%EX0:20000:FT$RE$:COSB:VA$"Y":KV$"Y"VA$"("(Y)")"H%EX2:20000:KV$"Y"(CO)1RE$(RE$,1)(RE$,3)H%7:21(FT$)(RE$):FT$;" ";RE$;" = ";SCI%7:3:570:1;::" OR ";::2;::"? ";CG+%G$:G$"1"G$"2"9515:G$;:sGD%SAA1:SBB1:SCC1:G$"2"SAA2:SBB2:SCC2GN%KVX:CKVSA:CSVSB:KV$"Y"KVY:CKVSB:CSVSAH%5400:"FIRST, REWRITE EQUATION ";::G$;::", REPLACING"::KV$;" WITH ";KV;".":53:KV$"X"SV$"Y"FF#9500EF#VA$RV$:VS12:CO(1)0:CO(2)C5:40000XF#KV$RV$:35000^FT$F%5400:"TO SOLVE FOR ";SV$;", YOU MUST SUBSTITUTE"::"FOR ";KV$;" IN ONE OF THE ORIGINAL EQUATIONS.":5300G&%5400:"SUBSTITUTE FOR "KV$" IN EQUATION ";::E~"C3;" + ";C4;" = ";C5:5300:V19:H1:NL4:5500:8800KE"10:3:3);qE"RV$"X":COA5:A50RV$"Y":COB5E"12:VA$RV$:EX0:20000:22(RE$):RE$;" = ";C5E"CO1KV$RV$:35000E"M13:E(# SOLV/VARE2#FOUND0SV$RV$:9100F<#SV$"X"5:10:22:" = ":19:1:C3;" + ";C4;" = ";:900:C2$G$:CH$C2$:6400:BADV19:H1:NL4:5500:8800Dj"(C2$)C5Ģ10:29((C5)):C5:5400:S60:8900Et"E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:8800Ģ10:18:EX2:20000:RE$:S60:V19:H1:NL4:5500:8800C"E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:8700C"COB3:20000:RE$;" + ";:COB4:20000:RE$;" = ";C1$:V19:H1:NL4:5300:5500:8700dD`"ZM9:H1:NL4:5300:5500:8600uB!COA3:20000:RE$;" + ";:COA4:20000:RE$;" = ";C1$:V19:H1:NL4:5300:5500:8600B!ZM5:19:1:VA$"Y":EX0:COB3:20000:RE$;" + ";:COB4:20000:RE$;" = ";:900:C2$G$:C2$""87008C"COB5:20000:C1$RE$:30000:C:19:1:VA$"X":EX0:COA3:20000:RE$;" + ";:COA4:20000:RE$;" = ";:900:C2$G$:C2$""8600A!COA5:20000:C1$RE$:30000:CĢ10:17(C1$):C1$:S60:V19:H1:NL4:5500:8700B!E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V140):V8:H13:25000t@17:1:"NOW COMPLETE THE SUBTRACTION BY ADDING"::"THE RESULTING EQUATIONS.":5300:5400~@4! ADD@>!5400@H!8:11:"+";@R!17:1:"ADD THE EQUATIONS TERM BY TERM."@\!A5A3A4:B5B3B4:C5C3C4@f!10:3:5700_A!ZM510:"--------------------"+?G$"1"85005? SUBO?8:11:"-";:3:5700?ZZ(34):34,16::34,ZZ:17:1:"TO SUBTRACT, YOU MUST CHANGE THE SIGNS"::"OF THE TERMS IN THE SUBTRAHEND.":5300:5400@A4A4:B4B4:C4C4:DAA4:DBB4:DCC4:8:1: THE FOLLOWING:":::"1) ADD THE EQUATIONS"::"2) SUBTRACT THE EQUATIONS":G$""|>^17:29:G$:G$"1"G$"2"8030:G$;>hG$"1"OKA3A40B3B40>rG$"2"OKA3A40B3B40>|OKER14(G$"2"):ZZ(34):34,16::34,ZZ:5950:8020?9:SAVE YOUR LOGO PROGRAM WITH THE":18:" FILENAME: HELLO."C (22: N@ : CLEAR SCREEN;@230,32:3086: CLEAR PAGE 1c@(13)(4);"BLOAD CBS.LOGO,A$2000"@49236,0: DISPLAY PAGE 1@#T13500:T@(::@2(13)(4)"RUN COVER"2GPRINT CHR$(13)CHR$(4)"(34)"RUN COVER"(34)9 16:" ?":Vt"OR PRESS ";::"ESCAPE";::" FOR NO CHANGE.":24:13:"PRESS <4>: ";:G$""q~G$:G$"4"1150:G$;5:13:"( 4X + 4Y = 20 ) / 4":34,6::16:"X + 5Y = 5":12:6:"NOW YOU MUST DIVIDE THROUGH."915:L$;:"DIVIDE #";::"2";::" TE4:5500:7835u:E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7805:RE$;" / ";D2;" = ";P2$(1):V19:H1:NL4:5300:5500:7805 ;ZM5:19:1:COB2:VA$"Y":EX0:20000:RE$;" / ";D2;" = ";:900:C2$G$:3:DAA2:DBB2:DCC2:25000:7900O9}5400:"DIVIDE #2 BY ";D2;" TERM BY TERM."k95:3:5700:8:3:57009ZM5:19:1:COA2:VA$"X":EX0:20000:RE$;" / ";D2;" = ";:900:C2$G$:C2$""7815:C1$P2$(1):30000:CĢ8:17(C1$):C1$:S60:V19:H1:NL$)C3Ģ7:29((C3)):C3:5400:S60:78008iE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN":V19:H1:NL4:5300:5500:77758nC1;" / ";D1;" = ";C3:5300:V19:H1:NL4:5500:7775 9x4:3:3);:7:3:3);:D21Ģ8:3:5700:V8:H1:"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:77557ZRE$;" / ";D1;" = ";P1$(2):V19:H1:NL4:5300:5500:77557_ZM5:7:22:" = ":19:1:C1;" / ";D1;" = ";:900:C2$G$:CH$C2$:6400:BADİ5500:7775*8d(C26FRE$;" / ";D1;" = ";P1$(1):V19:H1:NL4:5300:5500:77256KZM5:19:1:COB1:VA$"Y":EX0:20000:RE$;" / ";D1;" = ";:900:C2$G$:C2$""77556PC1$P1$(2):30000:CĢ7:18:COB3:VA$"Y":EX2:20000:RE$:S60:V19:H1:NL4:5500:7775Z7UE3E31:9:1:COA1:VA$"X":EX0:20000:RE$;" / ";D1;" = ";:900:C2$G$:C2$""77355<C1$P1$(1):30000:CĢ7:17(C1$):C1$:S60:V19:H1:NL4:5500:77555AE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7725=";C4:5300:V19:H1:NL4:5500:7555L45:3:3);:8:3:3);:MD1:M12:X4 DIV.b463004#D11Ģ7:3:5700:V7:H13:DAA1:DBB1:DCC1:25000:78004(S604-5400:"DIVIDE #1 BY ";D1;" TERM BY TERM."424:3:5700:7:3:5700L57ZM5:1 = ":19:1:MU(2);" * ";C2;" = ";:900:C2$G$:CH$C2$:6400:BADİ5500:75553(C2$)C4Ģ8:29((C4)):C4:5400:S60:76003E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN":V19:H1:NL4:5300:5500:7555$4MU(2);" * ";C2;" = 8:18:COB4:VA$"Y":EX2:20000:RE$:S60:V19:H1:NL4:5500:75552yE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:75352~MU(2);" * ";RE$;" = ";P2$(2):V19:H1:NL4:5300:5500:7535M3ZM5:8:22:"S INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:75051jMU(2);" * ";RE$;" = ";P2$(1):V19:H1:NL4:5300:5500:75051oZM5:19:1:COB2:VA$"Y":EX0:20000:MU(2);" * ";RE$;" = ";:900:C2$G$:C2$""7535D2tC1$P2$(2):30000:CPLY #2 BY "MU(2)" TERM BY TERM."<0V5:3:5700:8:3:57000[ZM5:19:1:COA2:VA$"X":EX0:20000:MU(2);" * ";RE$;" = ";:900:C2$G$:C2$""75150`C1$P2$(1):30000:CĢ8:17(C1$):C1$:S60:V19:H1:NL4:5500:7535I1eE3E31::"SORRY, THAT I"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7460/3MU(1);" * ";C1;" = ";C3:5300:V19:H1:NL4:5500:7460/L4:3:3);:7:3:3);:MU(2)1Ģ8:3:5700:V8:H13:DAA2:DBB2:DCC2:25000:7600 0Q5400:"MULTI:H1:NL4:5300:5500:7440].MU(1);" * ";RE$;" = ";P1$(2):V19:H1:NL4:5300:5500:7440.$ZM5:7:22:" = ":19:1:MU(1);" * ";C1;" = ";:900:C2$G$:CH$C2$:6400:BADİ5500:7460.)(C2$)C3Ģ7:29((C3)):C3:5400:S60:7500X/.E3E31::(4)"MAXFILES 1")F769,0:779,0P::10:16:"LOADING":12:6:"SIMULTANEOUS LINEAR EQUATIONS":(4);"RUN SIMLINEQ"S CHANGE.":24:13:"PRESS : ";:G$""CVG$:G$(27)1110s`1:4:" ";:16:"X + 5Y = 5":34,5::8j" WE CAN EQUALIZE THE COEFFICIENT OF X"::"BY DIVIDING THE EQUATION BY 4.":15:L$;:"DIVIDE EQUATION #";::"2";::" BY WHAT VALUE+ MULT.+6300U+MU(1)1Ģ7:3:5700:V7:H13:DAA1:DBB1:DCC1:25000:7500^+S60+5400:"MULTIPLY #1 BY "MU(1)" TERM BY TERM."+4:3:5700:7:3:5700,ZM5:19:1:COA1:VA$"X":EX0:20000:MU(1);" * ";RE$;" = ";:900:C2$G$:C2$"WILL MAKE THE COEFFICIENTS OF ";:(B1G2)(B2G2)G217372v*ER0ĺ"X EQUAL"::"TO ";ZZ;" OR ";ZZ;".":7374*ER0ĺ"Y EQUAL"::"TO ";ZG;" OR ";ZG;"."*ER0İ5300:5400:7245*D11D21ER13:5950:V4:H1:NL2:5500:*7700 B4)7380M)ER0ĭ(A1)(A2)(B1)(B2)ER22:5950:V4:H1:NL2:5500:v)ER0ĭD11D21ER11:5950:7245)ZZ0:ZG0:(A1G1)(A2G2)(B1G1)(B2G2)ZZA1G1:ZGB1G2?*ER0E1E11:5400:"DIVIDE THE EQUATIONS BY VALUES WHICH"::D2(G2D2)ER9:5950:7305](5:12:"(";:V5:H13:DAA2:DBB2:DCC2:25000:" ) / ";D2(AV$"":5:3:3);:5400:D10D11(D20D21(D11D217375(A3A1D1:B3B1D1:C3C1D1(A4A2D2:B4B2D2:C4C2D2)(A3)(A4)(B3)( ";D1'p5400+'4:3:3);:5:3:5700'ZM2:5400:17:1:R3$"2 "R2$::"OR PRESS ";::"RETURN";::" FOR NO CHANGE.":17:35:900:AV$"":D2(G$):D21G$""'G$""V5:H13:DAA2:DBB2:DCC2:25000:7350'D20ER10:5950:7305(G2S ";::"RETURN";::" FOR NO CHANGE.":17:35:AV$"N":900:D1(G$):D11G$""&WG$""V4:H13:DAA1:DBB1:DCC1:25000:7300&\D10ER10:5950:7250&aG1D1(G1D1)ER9:5950:7250'f4:12:"(";:V4:H13:DAA1:DBB1:DCC1:25000:" ) /%>ZZ%C5400v%HOK0:T11G1:T21G2:G1T1(G1T1)G2T2(G2T2)((A1T1)(A2T2)(B1T1)(B2T2))OK1%JT2,T1:OKER12:5950:%KER0%MR3$"DIVIDE EQUATION #":V4:H1:NL2:5500:4:3:5700P&RZM2:17:1:R3$"1 "R2$::"OR PRES:"TO "ZG".":5300:7018N$MU(1)1MU(2)1ER13:5950:V4:H1:NL2:5500:X$7400c$  DIVq$*G11:G21$/ZZ25:(A1ZZ)(A1ZZ)(B1ZZ)(B1ZZ)(C1ZZ)(C1ZZ)G1ZZ$0ZZ$4ZZ25:(A2ZZ)A2ZZ(B2ZZ)B2ZZ(C2ZZ)C2ZZG2ZZ129#ZZA1A26#B1B2B1B2(B1B2)ZGB1:7132\#B2B1B2B1(B2B1)ZGB2:7132i#ZGB1B2$ER0E1E11:5400:"MULTIPLY THE EQUATIONS BY VALUES WHICH":"WILL MAKE THE COEFFICIENTS OF X EQUAL":"TO "ZZ", OR THE COEFFICIENTS OF Y EQUAL"U(1)1MU(1)16"A3MU(1)A1:B3MU(1)B1:C3MU(1)C1^"A4MU(2)A2:B4MU(2)B2:C4MU(2)C2"(A3)(A4)(B3)(B4)7135"ER0MU(1)1MU(2)1ER4:5950:7018"ZZ0:ZG0:A1A2A1A2(A1A2)ZZA1:7129#A2A1A2A1(A2A1)ZZA2:7781):E1(782):E2(783):E3(784):TE(1)(785):TE(2)(786):TE(3)(787):A1128(788):A2128(789) B1128(790):B2128(791):C1128(792):C2128(793):DA128(794):DB128(795):DC128(796):X128(797):Y128(798):A$:G$"2"1080:G$; B34,3::7:" SINCE THE COEFFICIENT OF X IS ALREADY":"EQUAL TO 1 IN THE FIRST EQUATION, WE DO"::"NOT HAVE TO CHANGE IT."+L15:L$;:"DIVIDE EQUATION #";::"1";::" BY WHAT VALUE?"::"OR PRESS ";::"ESCAPE";::" FOR NO UGHT TO THE FOLLOWING"::"MENU. FOR THIS SAMPLE PROBLEM, WE CAN"::"USE DIVISION TO EQUALIZE THE"::"COEFFICIENTS OF X." .15:L$:"1) MULTIPLY EQUATION(S) BY A CONSTANT"::"2) DIVIDE EQUATION(S) BY A CONSTANT":400:16:"PRESS <2>: ";:G$"" 8G35,14:34,4:::" BEFORE WE CAN ADD OR SUBTRACT THE"::"EQUATIONS, WE MUST MULTIPLY OR DIVIDE"::"IN ORDER TO EQUALIZE THE COEFFICIENTS" :"OF X OR Y.";:400:16:"PRESS <1>: ";:G$"" G$:G$"1"1050:G$;| $35,24:::" NOW WE ARE BRO$",":10:3:"LET'S RUN THROUGH A SAMPLE PROBLEM":12:3:"TOGETHER.":100 :"SAMPLE ";::"1";::16:"X + 5Y = 5":8::"2";::15:"4X + 4Y = 20":L$ 8:" WHEN THE PROBLEM BEGINS, YOU WILL"::"SEE A MENU LIKE THE ONE BELOW.":200:100 0:V 15:L$:"1) MULTIPLY/DIVIDE ";::"1";::" OR ";::"2";::" BY A CONSTANT" :"2) ADD OR SUBTRACT EQUATIONS"::"3) SOLVE FOR VARIABLE X OR Y": ,G$:G$(13)300: 24:1:39);:24:1: 500J 35,24:33,40:34,0::7:3:N"RETURN";::" FOR NO CHANGE.":17:37:1000:MU(2)(G$):MU(2)1G$""c S30:MU$G$:IN1S31x (G$)0MU$G1$ S11(MU$)13MU(2)1:7057 S11S31MU(2)1ER6:5950:7050 S11MU(2)1ER5:5950:V4:H1:NL2:5500:!MU$$)64(MU$)487015YsMU(1)0MU(1)1V4:H13:DAA1:DBB1:DCC1:25000:MU(1)1:7045ruV4:H12((MU(1)))vV:H:MU(1);"(";:H13:DAA1:DBB1:DCC1:25000:" )"5400:4:3:" ":5:3:5700G ZM2:17:1:R1$"2 "R2$::"OR PRESS ";::1$"1 "R2$::"OR PRESS ";::"RETURN";::" FOR NO CHANGE.":17:37:1000:MU(1)(G$):MU(1)1G$""mS30:MU$G$:IN1S31n(G$)0MU$G1$oS11(MU$)13MU(1)1:7027pS11MU(1)1ER5:5950:qMU$"0"ER3:5950:7010r(MU,1):(ZZ$"0"ZZ$"9")ZZ$"+"ZZ$"-"ZZ$" "BAD1AZZ:ZX COR VAL-MAIN MENUw]5400:IN7010,8000,9000bER0:5050:R1$"MULTIPLY EQUATION #":R2$"BY WHAT VALUE?"gG327200j5400:V4:H1:NL2:5500:4:3:5700dlZM2:17:1:R(ER)f5300:5400:* COR ANS-MULTSVA$"X":COA3:EX0:20000:P1$(1)RE$wVA$"Y":COB3:20000:P1$(2)RE$VA$"X":COA4:20000:P2$(1)RE$VA$"Y":COB4:20000:P2$(2)RE$:CHECK FOR NON-NUMERIC7 BAD0:ZZ1(CH$):ZZ$(CH$,ZZ5950:%M12IN1MDER7:5950:CM13IN3ER16:5950:TD REV.ARROWcN:AR$::w> ERROR MESSAGEHM11M12E1E11:5980RE2E21\5400:(ER$(ER))120āZZ0((ER$(ER))40.01):(ER$(ER),140ZZ,40):ZZ:5990aER$141ī5320(16368,0:24:7:30);:> ERASE MAIN MENUW"34,16:19::34,0:p| ERASE PARTS SCREEN34,V1:35,VNL1:V::34,0:35,24: MENU ERRORSER0:540017:1M11(IN2IN3)ER1:5950:M12IN3ER2:LE X OR Y":F717:1:"ENTER ONE OF THE FOLLOWING:";::" ";:G1$""Y8G1$:IN(G1$)u<IN1IN35176:G1$;:P LINEdV:1:ZZ139:"-";:ZZ: RETURN16368,0:24:8:"PRESS ";::"RETURN";::" TO CONTINUE. "; (16384)E EQUATION(S) BY A CONSTANT":G1$"":17:29NG1$:G3(G1$):G30G325070ZG1$;:j MAIN MENU{5400:19:1"1) MULTIPLY/DIVIDE ";::1;::" OR ";::2;::" BY A CONSTANT": "2) ADD OR SUBTRACT EQUATIONS"::"3) SOLVE FOR VARIAB)"-"ZG010103G$G$G1$:ZGZG1:G1$;:1010BZG01010_(8)" "(8);:ZG11000 ZGZG1:G$(G$,(G$)1):1010 MULT/DIV5400:G30+:"ENTER ONE OF THE FOLLOWING:":::"1) MULTIPLY EQUATION(S) BY A CONSTANT"::"2) DIVID" "(8);:ZZ19004G$(G$,(G$)1):ZZZZ1:910OG$"":ZH0:ZG0:G1$""mG1$:ZH(G1$):ZH81030ZH13ĭG$"-"1010ZH13ıG1$"-"ZG0ZGZG1:G1$;:G$G$G1$:1010ZH49ZH571010(G$,1)"-"ZG11010(G$,1ZH)"(ZH88ZH89)AV$"N"910PZH47ZH58ĭ(G$,1)"X"(G$,1)"Y"910qZH43ZH45ZH88ZH89928ZH47ZH57910ZZ0930:G1$"X"G1$"Y"āX51(G$):(G$,X5,1)G1$910:ZZZZ1:G1$;:G$G$G1$:910ZZ0900(8)(G$));G$:%G1$"":G$"":ZZ0:ZH0^G1$:ZH(G1$):ZH13Ĵ(G$,1)"-"(G$,1)"+"910:~G1$"-"G1$"+"ĭZZ0910ZH8940ZZZMG$"0"G$"-0"G$"+0"910G1$"0"ĭ(G$,1)"-"(G$,1)"+"910ZH120ZH121ZHZH32:G1$((2):787,TE(3):788,128A1:789,128A2:790,128B1ٹ791,128B2:792,128C1:793,128C2:794,128DA:795,128DB:796,128DC:797,128X:798,128Y:ٲ RESTORE VARIABLESفZZ768778:ZH(ZZ):ZH055810:N$N$(ZH):eRC%(779):P%(780):N%( SAMPLE/ BY KEVIN VESSIO - 9/20/84aL$"----------------------------------------"rN$"":ZZ769((ZZ)0N$N$((ZZ)):ZZZZ1:4021000d24:9:"PRESS ";::"RETURN";::" TO CONTINUE.";:16368,0 n(16384)1281311       !" " " "  4"COMPUTATIONAL ERRORS ...... ";:ZZTE(3):800w::"GRAND TOTAL ............... ";:ZZTE(1)TE(2)TE(3):800::7)"YOU COMPLETED "P%" PROBLEM";:P%1ĺ".":730"S."5300:55000:10:10(N$)2:"WE'RE ALL DONE NOW, ";N$;".:"TOTAL ERROR ANALYSIS":::33)"AVERAGE";:35)"PER":" ERROR NUMBER PROBLEM";" ----- ------ -------";:"ELIMINATING A VARIABLE .... ";:ZZTE(1):800:"SOLVING LINEAR EQUATIONS .. ";:ZZTE(2):800:E1:TE(2)TE(2)E2:TE(3)TE(3)E3:ZZ(0):P%N%İ5300:70022:" PRESS ";::"RETURN";::" FOR NEXT PROBLEM."::12:"PRESS ";::"Q";::" TO QUIT.";16384,128:ZZ(16384)128:16368,0:ZZ81ZZ113700ZZ13660200d:11b"ELIMINATING A VARIABLE ........ ";E1::"SOLVING LINEAR EQUATIONS ...... ";E2:q"COMPUTATIONAL ERRORS .......... ";E3:31);"---"::"TOTAL ......................... ";E1E2E3v19:ME$(3((E1E2E30)(E1E2E31))(3(1))):TE(1)TE(1) SOLUTION BY"::"GRAPHING THE EQUATIONS.":24:12:"ONE MOMENT, PLEASE.";:22::(4);"BLOAD CHAIN, A520":520"GRAPH"X:7:"ERROR SUMMARY FOR PROBLEM #";P%::::" ERROR NUMBER"]" ----- ------":S"::"I'LL CHECK EQUATION ";::1;::".":CH1:5300:45000 05400:"NEXT, I'LL CHECK EQUATION ";::2;::".":CH2:5300:45000 :5400:"SINCE THE SOLUTION CHECKS IN BOTH"::"EQUATIONS, WE KNOW IT'S CORRECT.":5300vD5400:"WE CAN ALSO CHECK THELVE": 1:7::"1"( 2:7:"2":p V1:H13:DAA1:DBB1:DCC1:25000:V2:H13:DAA2:DBB2:DCC2:25000~ V3:5200 V16:5200 ER0:5100 5600:ER500 ER0:7000 FOUND2500; &5400:"NOW, I'LL CHECK YOUR ANSWER. FIRST,(R):A10320$ JA2R(R):A20330; TB1R(R):B10340R YB2R(R):B20345h \M11:MD0:FOUND0 ^S10:(A1)(A2)(B1)(B2)S11:M12 `A1B1A2B2320 cR10:XR(R):YR(R) eX0Y0355 hC1A1XB1Y:C2A2XB2Y |::"SONS.":5300 Z55000q d:3:N$",":::"YOU MAY TRY UP TO 9 PROBLEMS."::"HOW MANY WOULD YOU LIKE? ";:G1$"" nG1$:N%(G1$):N%0110:G1$:P%0 R(X)((1)X1)X2 AR$"-->" DO N% PROBLEMS P%P%1:E10:E20:E30:R10 @A1R2$"":CO0:CH$"":VA$"":RE$""C >N$"":ZZ(769):ZZ080:ZH769o @ZZ(ZH):ZZ0N$N$(ZZ):ZHZH1:64~ B10000:90 P50000:51000:10000 R:4:"HI, "N$"!":::"THIS PROGRAM WILL HELP YOU PRACTICE"::"SOLVING SIMULTANEOUS LINEAR EQUATIO{~33,40:34,0$ SIMULTANEOUS< LINEAR EQUATIONS T COPYRIGHT (C) 1983rMICROCOMPUTER WORKSHOPS PORTCHESTER, NY LAST UPDATE: 9/25/84 BY: KEVIN VESSIO2RC%6007ER$(22),ME$(8) <ZZ0:ZZ$"":Z$"":Z1$"":C1$"":CY";:ZZ769pXفX1(N$):ZZ,((N$,X,1)):ZZZZ1::ZZ,0:15:11:"ONE MOMENT, PLEASE.":(13)(4)"RUN SAMPLE"ٲ SAVE VARIABLES2ZZ768:ZH1(N$):ZZ,((N$,ZH,1)):ZZZZ1::ZZ,0:779,0:780,P%:781,N%:782,E1:783,E2:784,E3:785,TE(1):786,TE;:5400:D10D11!+D20D215+D11D217375T+A3A1D1:B3B1D1:C3C1D1s+A4A2D2:B4B2D2:C4C2D2+(A3)(A4)(B3)(B4)7380+ER0ĭ(A1)(A2)(B1)(B2)ER22:5950:V4:H1:NL2:5500:,ER0ĭD11D21ER11:5950:7.":17:35:W91:900:W90:AV$"":D2(G$):D21G$""h*G$""V5:H13:DAA2:DBB2:DCC2:25000:7350*D20ER10:5950:7305*G2D2(G2D2)ER9:5950:7305*5:12:"(";:V5:H13:DAA2:DBB2:DCC2:25000:" ) / ";D2+AV$"":5:3:3):7300")\D10ER10:5950:7250H)aG1D1(G1D1)ER9:5950:7250)f4:12:"(";:V4:H13:DAA1:DBB1:DCC1:25000:" ) / ";D1)p5400)4:3:3);:5:3:57005*ZM2:5400:17:1:R3$"2 "R2$::"OR PRESS ";::"ESCAPE";::" FOR NO CHANGEER12:5950:(KER0Q(MR3$"DIVIDE EQUATION #":V4:H1:NL2:5500:4:3:5700(RZM2:17:1:R3$"1 "R2$::"OR PRESS ";::"ESCAPE";::" FOR NO CHANGE.":17:35:AV$"N":W91:900:W90:D1(G$):D11G$"")WG$""V4:H13:DAA1:DBB1:DCC1:25000(A1ZZ)(B1ZZ)(B1ZZ)(C1ZZ)(C1ZZ)G1ZZ8'0ZZx'4ZZ25:(A2ZZ)A2ZZ(B2ZZ)B2ZZ(C2ZZ)C2ZZG2ZZ'>ZZ'C5400'HOK0:T11G1:T21G2:G1T1(G1T1)G2T2(G2T2)((A1T1)(A2T2)(B1T1)(B2T2))OK1 (JT2,T1:OK4:5950:7018b&MU(1)1MU(2)1Ĵ(A1)(A2)(B1)(B2)7136:ER13:5950:V4:H1:NL2:5500:&MU(1)1MU(2)1ER5:5950:V4:H1:NL2:5500:&(A3)(A4)(B3)(B4)ER4:5950:7018&7400&  DIV&*G11:G210'/ZZ25:(A1ZZ)7132*%B2B1B2B1(B2B1)ZGB2:71327%ZGB1B2%ER0E1E11:5400:"MULTIPLY THE EQUATIONS BY VALUES WHICH":"WILL MAKE THE COEFFICIENTS OF X EQUAL":"TO "ZZ", OR THE COEFFICIENTS OF Y EQUAL":"TO "ZG".":5300:7018&MU(1)1MU(2)1ER)C1,$A4MU(2)A2:B4MU(2)B2:C4MU(2)C2N$(A3)(A4)(B3)(B4)7135{$ER0MU(1)1MU(2)1ER4:5950:7018$ZZ0:ZG0:A1A2A1A2(A1A2)ZZA1:7129$A2A1A2A1(A2A1)ZZA2:7129$ZZA1A2%B1B2B1B2(B1B2)ZGB1:5P#S40:MU(2)0MU(2)1V5:H13:DAA2:DBB2:DCC2:25000:S41:MU(2)1:7100i#V5:H12((MU(2)))#V:H:MU(2);"(";:H13:DAA2:DBB2:DCC2:25000:" )"#5:3:" "#5400#MU(1)0MU(1)1MU(1)1$A3MU(1)A1:B3MU(1)B1:C3MU(1(G$):MU(2)1G$""1"S30:MU$G$:IN1S31F"(G$)0MU$G1$h"S11(MU$)13MU(2)1:7057"S11S31MU(2)1ER6:5950:7050"S11MU(2)1ER5:5950:V4:H1:NL2:5500:"MU$"0"ER3:5950:7045#(MU$)64(MU$)48704B1:DCC1:25000:MU(1)1:70456!uV4:H12((MU(1)))q!vV:H:MU(1);"(";:H13:DAA1:DBB1:DCC1:25000:" )"!5400:4:3:" ":5:3:5700"ZM2:17:1:R1$"2 "R2$::"OR PRESS ";::"ESCAPE";::" FOR NO CHANGE.":17:37:W91:1000:W90:MU(2)1:1000:W90:MU(1)(G$):MU(1)1G$""D mS30:MU$G$:IN1S31Y n(G$)0MU$G1${ oS11(MU$)13MU(1)1:7027 pS11MU(1)1ER5:5950: qMU$"0"ER3:5950:7010 r(MU$)64(MU$)487015!sMU(1)0MU(1)1V4:H13:DAA1:DBв COR VAL-MAIN MENU1]5400:IN7010,8000,9000obER0:5050:R1$"MULTIPLY EQUATION #":R2$"BY WHAT VALUE?"~gG327200j5400:V4:H1:NL2:5500:4:3:5700( lZM2:17:1:R1$"1 "R2$::"OR PRESS ";::"ESCAPE";::" FOR NO CHANGE.":17:37:W900:P1$(1)RE$1VA$"Y":COB3:20000:P1$(2)RE$UVA$"X":COA4:20000:P2$(1)RE${VA$"Y":COB4:20000:P2$(2)RE$:CHECK FOR NON-NUMERIC BAD0:ZZ1(CH$):ZZ$(CH$,ZZ,1):(ZZ$"0"ZZ$"9")ZZ$"+"ZZ$"-"ZZ$" "BAD1ZZ:XD REV.ARROWN:AR$::1> ERROR MESSAGENHM11M12E1E11:5980ZRE2E21\5400:(ER$(ER))120āZZ0((ER$(ER))40.01):(ER$(ER),140ZZ,40):ZZ:5990aER$(ER)f5300:5400: COR ANS-MULT VA$"X":COA3:EX0:200,16:19::34,0:*| ERASE PARTS SCREENU34,V1:35,VNL1:V::34,0:35,24:g MENU ERRORSvER0:540017:1M11(IN2IN3)ER1:5950:M12IN3ER2:5950:M12IN1MDER7:5950:M13IN3ER16:5950:(8)5176:IN(G1$)/<IN1IN35176:G1$;:;P LINEZdV:1:ZZ139:"-";:ZZ:h RETURN16368,0:24:8:"PRESS ";::"RETURN";::" TO CONTINUE. ";(16384)141ī532016368,0:24:7:30);: ERASE MAIN MENU"34"N$"!"::(41(G$))2:G$:::11:"ONE MOMENT, PLEASE."Xr(13)(4)"RUN SIMLINEQ"IN MENU&5400:4:3:" ";:19:1o"1) MULTIPLY/DIVIDE ";::1;::" OR ";::2;::" BY A CONSTANT":"2) ADD OR SUBTRACT EQUATIONS"::"3) SOLVE FOR VARIABLE X OR Y":717:1:"ENTER ONE OF THE FOLLOWING:";::" ";:G1$""8G1$:G1$OUS LINEAR EQUATIONS":(4);"RUN SIMLINEQ":GRAPH THE EQUATIONS."::"THE POINT OF INTERSECTION IS THE"::"SOLUTION TO THE EQUATIONS.":100hG$"GOOD LUCK, "N$"!"::(41(G$))2:G$:::11:"ONE MOMENT, PLEASE."r779,0:(13)(4)"RUN SIMLINEQ"1THE EQUATIONS.":100;hG$"GOOD LUCK, $,(G$)1):1010  MULT/DIV/5400:G30:"ENTER ONE OF THE FOLLOWING:":::"1) MULTIPLY EQUATION(S) BY A CONSTANT"::"2) DIVIDE EQUATION(S) BY A CONSTANT":G1$"":17:29G1$:G1$(8)5070:G3(G1$):G30G325070G1$;: MA 膢 ȱ " <67 L  8ij v vo>BFIKMOQSUY[]_acegikmoqsuwy{} <"<"""<< <"""<"><$""< """"  "" 6***""""""""""<""< :< $"""2,"""""**6"""""< >>8  80,"*:<"">""""""""""""">>><2"<""">""" ""  ">"6**"""""&*2""""""""""""*,"" "" ">""""""""""""""**6"""""""> >>> >00000>">>< (&20 *, **>> "2*&" " >>  ">> "8""> """"""< >> "$$! $%%#,fp% "Lp"% $`"H Β*+)hi#"H Β!*0+i+idH#d hd`"%$$%H hi#`$% Βc,d*+Me,dPMc*!0 +i+`%J) b+je *`PPPP򠥹,r0tL"$!e (' !!%##`f`" e$$ ",r0st(!#L"L $b . % `L a,gPgA[8 & & &mh)mi ̒e$*+Me$(Mc,dp ,cpP!pA* +i+Mebrs"t`,Tb@0,U`* L" {LB$!$$"% %L"c`g`g`,,Lҩc`@a`de` qLXde`s$t%L$td`e`g`f`Yd`e`L$e (' 8!$!$%"{LȎ !%# "LȎ5 )5`)aW L| JHIHa`G~ҏ#+@HPXs{ɐG֐G+R$a`1  emhi` b` ,r0rbj$s%t`@b`s$$hLde`,rSjd LL LHLH C `u8967 ,R,W U ,P`ɭӠҠΠΠ Р̺((*)  b+*HN OI*P,h*,H,`0ɛ` ɍ $h`ɐ 6+` qLȎ LȎ      HȑnhmȑstLS g ^ m  ` ^LLg L@A8m  @0 /@   q@8 @8e@@AiAP`L2Ġ JJJJHȱH ȩȩȩȑhhȩȩȑ /"& &  "  gLS) LSȩȩȩ ȩȩȩ gȭX Y Z [ \ ] hhh`HH ' hh^ `HHHV  V ` Lhhh`,n àϠȥ𬠄𠠠ŠϠÊәĠ̠ m ` 18)`8`HHH n  V H$hb V W X Y m [ l \ ] S ^ T _  ' hhh`HHV ' b i-c ihh`HH$Hȱhhh` LHHHHHHV W L m m  뭒 L   m   (m , r0+p  LJ  LJ -  ȱ  LJ ȱ  LJ s tL m JJJJl ȱm n   ,L, L%" n  :, " +, S l L\DЪ m L\        s t   ަL !8  PL(1,1)7:PL(1,2)0:PL(2,1)7:PL(2,2)0:62000d\PL(1,1)0:PL(1,2)7:PL(2,1)0:PL(2,2)7:620000:PL(1,1)7:PL(1,2)0:62500:416:PL(1,1)0:PL(1,2)7:62500:432:PL(1,1)7:PL(1,2)0:62500:448:PL(1,1)0:PL(1,2)7:62500:4NES INTERSECT,IN THIS CASE (";X;",";Y;"), IS THE SOLUTION":"TO THE SYSTEM OF EQUATIONS.":5300:::(4);"PR#0":(4);"IN#0":OLDHI:OLDHI(0)RC%1:::12:11:"ONE MOMENT, PLEASE.":15000:(13)(4)"RUN SIMLINEQ"HSETUP AXESM3:10R77.25:PL(2,1)ZZ:PL(2,2)(C2A2ZZ)B2:(PL(2,2))7ĂZZH62000R5300eX0Y060500PL(1,2)Y:ZZX0(.3333(X)):PL(1,1)ZZ:62500:ZZPL(1,1)X:ZZY0(.3333(Y)):PL(1,2)ZZ:62500:ZZ_T5400:"THE POINT WHERE THE TWO LI:PL(2,2)(C1A1ZZ)B1:(PL(2,2))7ĂZZ3Z62000=d5300x5400:"NEXT, PLOT ";:VA$"X":COA2:60150:B20ĺ"+";VA$"Y":COB2:60150:VA$"":COC2:60150:"."5300ZZ77.25:PL(1,1)ZZ:PL(1,2)(C2A2ZZ)B2:(PL(1,2))7ĂZZ=ZZ))CO;VA$;:'3:192,0192,16279,16c(5400:"FIRST, PLOT ";:VA$"X":COA1:60150:B10ĺ"+";-VA$"Y":COB1:60150:VA$"":COC1:60150:"."<5300FZZ77.25:PL(1,1)ZZ:PL(1,2)(C1A1ZZ)B1:(PL(1,2))7ĂZZ(PZZ77.25:PL(2,1)ZZz# ??      ĠԠǠ Ӡ Ҡ Ϡ Š ӮϠ" Ϯà Ҡ!ѠϠy"Ƞ8p@?`@@`??`@`?`88`8axxx켌@yYa8`8008O@ฮ꺎C @p~8p`@@@@ ꊂx ՟~||p@p@1ƚagfga``cfgfgccg`g@p|s@`p0  80`@p300p0030\xppฮ|@@`p8p`p|Օ@p`p8`p p pxฮB|p p `?``Օa@: @@8`7 7 S S S S 0p06 p@9 `88 0<710 @# Ff@@~~" 8p`@@@@@@`p0? @@@`p8@s0`@xy?``? 80p``@@@@@``00 x x x8` |  c``ag# #  ??# g``c```g7  LLOLLL  XpxC `0 @!~cffc```@x | Cx q33s3331!`?@xx윀@8yյCp@0800OꚆa`8~ 0`@``յC@@`0 ``Ꚇa F~~8`8`ccffc``agCffCaGqCf`fC`xN<8`@?`@@@ppqx@|뛇p``0 ?`?@յ|?``?px x xꚆaxx x @@յC?`xppꚆ` ! S S pp07 8`: @p9 8>30 @$ FfF@ #  0`@@@@`0? @@`0 a303a `08  0p`@q30p0031 Xp   LOC24831:UNPACK768B #0,LOC((LOC256)256):1,(LOC256)N $230,64n ((4);"BLOAD LOGO.PAC,A"LOCz 2UNPACK <4:0,110,1 F16304,0:16297,0:16302,0:16299,0:769,0:779,0* PZ12500:Z:::10:16:"LOADING":12:6:"SIMULTANE, REVISED 3/7/84 BY J.P A. LOGO ADDED B. INTERMEDIATE FILES DELETED C. DISK VOL # CHANGED TO DEFAULT NOTE:PROBLEM W/DELETING REL HRCG DUE TO OTHER CHAR SETS (4)"MAXFILES 1"230,32:62450:230,64:62450 :(4);"BLOAD UNPACKER"  "+"8cG$"S"G$"s"G$"-"=8hG$"+"OKA3A40B3B40\8rG$"-"OKA3A40B3B408|OKER14(G$"-"):5950:802089:10:"--------------------"8G$"+"85008SUBTRACT THE EQUATIONS88:11:"-";:3:5700P917:1:"TO SUBTR3B1:C3C1:A4A2:B4B2:C4C2:V7:H13:DAA3:DBB3:DCC3:25000:V8:H13:DAA4:DBB4:DCC4:250007T17:1:"WILL YOU ADD OR SUBTRACT (+ OR -)?";:V17:H36:5800:G$(G$,1):G$"+"G$"-"G$"A"G$"S"G$"a"G$"s"İ5400:80208^G$"A"G$"a"G$G$:CH$C2$:6400:BAD7565O6(C2$)C4Ģ8:29((C4)):C4:5400:S60:76006E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:75556MU(2);" * ";C2;" = ";C4:5300:V19:H1:NL4:5500:755575:3:V19:H1:NL4:5500:75555yE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:75355~MU(2);" * ";RE$;" = ";P2$(2):V19:H1:NL4:5300:5500:75356ZM5:8:22:" = ":19:1:MU(2);" * ";C2;" = ";:900:C2$19:H1:NL4:5300:5500:7505`4jMU(2);" * ";RE$;" = ";P2$(1):V19:H1:NL4:5300:5500:75054oZM5:19:1:COB2:VA$"Y":EX0:20000:MU(2);" * ";RE$;" = ";:900:C2$G$:C2$""75355tC1$P2$(2):30000:CĢ8:18:COB4:VA$"Y":EX2:20000:RE$:S60:5700:8:3:5700l3[ZM5:19:1:COA2:VA$"X":EX0:20000:MU(2);" * ";RE$;" = ";:900:C2$G$:C2$""75153`C1$P2$(1):30000:CĢ8:17(C1$):C1$:S60:V19:H1:NL4:5500:75354eE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V"TRY AGAIN.":V19:H1:NL4:5300:5500:7460i23MU(1);" * ";C1;" = ";C3:5300:V19:H1:NL4:5500:74602L4:3:3);:7:3:3);:MU(2)1Ģ8:3:5700:V8:H13:DAA2:DBB2:DCC2:25000:76002Q5400:"MULTIPLY #2 BY "MU(2)", TERM BY TERM."3V5:3:);" * ";RE$;" = ";P1$(2):V19:H1:NL4:5300:5500:74401$ZM5:7:22:" = ":19:1:MU(1);" * ";C1;" = ";:900:C2$G$:CH$C2$:6400:BAD74701)(C2$)C3Ģ7:29((C3)):C3:5400:S60:7500,2.E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ:MU(1);" * ";RE$;" = ";:900:C2$G$:C2$""74400C1$P1$(2):30000:CĢ7:18:COB3:VA$"Y":EX2:20000:RE$:S60:V19:H1:NL4:5500:74600E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:744081MU(117(C1$):C1$:S60:V19:H1:NL4:5500:7440/E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7415/ MU(1);" * ";RE$;" = ";P1$(1):V19:H1:NL4:5300:5500:741510ZM5:19:1:COB1:VA$"Y":EX0:200003:5700:V7:H13:DAA1:DBB1:DCC1:25000:75008.S60k.5400:"MULTIPLY #1 BY "MU(1)", TERM BY TERM.".4:3:5700:7:3:5700.ZM5:19:1:COA1:VA$"X":EX0:20000:MU(1);" * ";RE$;" = ";:900:C2$G$:C2$""7420-/C1$P1$(1):30000:CĢ7:3744-ER0ĺ"Y EQUAL"::"TO ";ZG;" OR ";ZG;"."Q-ER0İ5300:5400:7245-D11D21Ĵ(A1)(A2)(B1)(B2)7376:ER13:5950:V4:H1:NL2:5500:-D11D21ER5:5950:V4:H1:NL2:5500:-7700- MULT.-6300/.MU(1)1Ģ7:245H,ZZ0:ZG0:(A1G1)(A2G2)(B1G1)(B2G2)ZZA1G1:ZGB1G2,ER0E1E11:5400:"DIVIDE THE EQUATIONS BY VALUES WHICH"::"WILL MAKE THE COEFFICIENTS OF ";:(B1G2)(B2G2)G217372-ER0ĺ"X EQUAL"::"TO ";ZZ;" OR ";ZZ;".":7 (0 Zнй`)JJ & & f)` "  ??" g```c```g6 : ?`@`?p@6 6 S 2aՀ  p333s3330?`C@`?x@!`yp`p 00``@@@@@``p08 p ppp@ |  accca``cf"aՀ `p8꺎C  LLLOLLL \xp ս Հ x~~`p8~C @agfga```@@p | xF"E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:8700F"COB3:20000:RE$;" + ";:COB4:20000:RE$;" = ";C1$:V19:H1:NL4:5300:5500:8700G`"ZM5:10:22:" = ":19:1:C3;" + ";C4;" = ";:900:C2$G$:CHCOA4:20000:RE$;" = ";C1$:V19:H1:NL4:5300:5500:8600E!ZM5:19:1:VA$"Y":EX0:COB3:20000:RE$;" + ";:COB4:20000:RE$;" = ";:900:C2$G$:C2$""8700E"COB5:20000:C1$RE$:30000:CĢ10:18:EX2:20000:RE$:S60:V19:H1:NL4:5500:8800e:RE$;" = ";:900:C2$G$:C2$""8600{D!COA5:20000:C1$RE$:30000:CĢ10:17(C1$):C1$:S60:V19:H1:NL4:5500:8700D!E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:8600;E!COA3:20000:RE$;" + ";:TION BY ADDING"::"THE RESULTING EQUATIONS.":5300:5400CC4! ADDMC>!5400^CH!8:11:"+";CR!17:1:"ADD THE EQUATIONS, TERM BY TERM."C\!A5A3A4:B5B3B4:C5C3C4Cf!10:3:5700%D!ZM5:19:1:VA$"X":EX0:COA3:20000:RE$;" + ";:COA4:200008:11:"-";:3:5700BZZ(34):34,16::34,ZZ:17:1:"TO SUBTRACT, YOU MUST CHANGE THE SIGNS"::"OF THE TERMS IN THE SUBTRAHEND.":5300:5400BA4A4:B4B4:C4C4:DAA4:DBB4:DCC4:8:1:40):V8:H13:250009C17:1:"NOW COMPLETE THE SUBTRACT THE EQUATIONS":G$""AA^17:29:G$:G$"1"G$"2"8030:G$;`AhG$"1"OKA3A40B3B40ArG$"2"OKA3A40B3B40A|OKER14(G$"2"):ZZ(34):34,16::34,ZZ:5950:8020A9:10:"--------------------"AG$"1"8500A SUBB:7855.@5:3:3);:8:3:3);:MD1:M12:8@@ +/-@JMDA3A1:B3B1:C3C1:A4A2:B4B2:C4C2:V7:H13:DAA3:DBB3:DCC3:25000:V8:H13:DAA4:DBB4:DCC4:25000AT17:1::"ENTER ONE OF THE FOLLOWING:":::"1) ADD THE EQUATIONS"::"2) SUBTRAC/ ";D2;" = ";:900:C2$G$:CH$C2$:6400:BAD7865e?(C2$)C4Ģ8:29((C4)):C4:5400:S60:7900?E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7855@C2;" / ";D2;" = ";C4:5300:V19:H1:NL4:5500$"Y":EX2:20000:RE$:S60:V19:H1:NL4:5500:7855>E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7835>RE$;" / ";D2;" = ";P2$(2):V19:H1:NL4:5300:5500:78351?ZM5:8:22:" = ":19:1:C2;" CT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7805=RE$;" / ";D2;" = ";P2$(1):V19:H1:NL4:5300:5500:7805=ZM5:19:1:COB2:VA$"Y":EX0:20000:RE$;" / ";D2;" = ";:900:C2$G$:C2$""78355>C1$P2$(2):30000:CĢ8:18:COB4:VA BY ";D2;", TERM BY TERM."6<5:3:5700:8:3:5700<ZM5:19:1:COA2:VA$"X":EX0:20000:RE$;" / ";D2;" = ";:900:C2$G$:C2$""7815<C1$P2$(1):30000:CĢ8:17(C1$):C1$:S60:V19:H1:NL4:5500:7835@=E3E31::"SORRY, THAT IS INCORRE:"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7775;nC1;" / ";D1;" = ";C3:5300:V19:H1:NL4:5500:7775;x4:3:3);:7:3:3);:D21Ģ8:3:5700:V8:H13:DAA2:DBB2:DCC2:25000:7900<}5400:"DIVIDE #2RY AGAIN.":V19:H1:NL4:5300:5500:7755i:ZRE$;" / ";D1;" = ";P1$(2):V19:H1:NL4:5300:5500:7755:_ZM5:7:22:" = ":19:1:C1;" / ";D1;" = ";:900:C2$G$:CH$C2$:6400:BAD7785:d(C2$)C3Ģ7:29((C3)):C3:5400:S60:7800Z;iE3E31:0:5500:7725e9KZM5:19:1:COB1:VA$"Y":EX0:20000:RE$;" / ";D1;" = ";:900:C2$G$:C2$""77559PC1$P1$(2):30000:CĢ7:18:COB3:VA$"Y":EX2:20000:RE$:S60:V19:H1:NL4:5500:7775*:UE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"T ";:900:C2$G$:C2$""7735g8<C1$P1$(1):30000:CĢ7:17(C1$):C1$:S60:V19:H1:NL4:5500:77558AE3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:7725 9FRE$;" / ";D1;" = ";P1$(1):V19:H1:NL4:5303);:8:3:3);:MD1:M12:'7 DIV.176300o7#D11Ģ7:3:5700:V7:H13:DAA1:DBB1:DCC1:25000:7800x7(S607-5400:"DIVIDE #1 BY ";D1;", TERM BY TERM."724:3:5700:7:3:570087ZM5:19:1:COA1:VA$"X":EX0:20000:RE$;" / ";D1;" =TTERM ON THE LEFT SIDE OF THE EQUATION."V'ER$(19)"MULTIPLYING BY A NUMBER WHOSE ABSOLUTE VALUE IS GREATER THAN 1 WILL NOT HELP TOSIMPLIFY THE EQUATION."V'ER$(20)"MULTIPLYING BOTH SIDES BY ONE WILL HAVE NO EFFECT ON THE EQUATION.">W'ER$(21)"DIVIER$(17)"TO SOLVE FOR THE VALUE OF THE VARIABLE, YOU MUST ELIMINATE ITS COEFFICIENT BY USING MULTIPLICATION OR DIVISION."(V'ER$(18)"BEFORE YOU CAN ELIMINATE THE COEFFICIENTOF THE VARIABLE, YOU MUST USE ADDITION OR SUBTRACTION TO ELIMINATE THE CONSTANND THE SOLUTION."gTj'ER$(14)"ADDING THESE EQUATIONS WILL NOT ELIMINATE ONE OF THE VARIABLES."Tt'ER$(15)"SUBTRACTING THESE EQUATIONS WILL NOT "(ER$(14),41)T~'ER$(16)"YOU'RE ALMOST DONE. THE NEXT STEP IS TOSOLVE FOR EITHER X OR Y."{U'L'ER$(11)"THE CONSTANTS YOU CHOSE TO DIVIDE BY "(ER$(4),41)SV'ER$(12)"THERE ARE NO WHOLE DIVISORS WHICH WILL ALLOW YOU TO GET EQUAL COEFFICIENTS FOR THE X OR Y VARIABLE."T`'ER$(13)"LEAVING BOTH EQUATIONS THE SAME DOES NOTHING TO HELP YOU FIR$(8)"THE MULTIPLIER YOU HAVE CHOSEN WILL GIVEYOU FRACTIONS IN THE EQUATION."R8'ER$(9)"YOUR DIVISOR WILL NOT DIVIDE EVENLY INTO ALL THE COEFFICIENTS. THIS WILL RESULT IN FRACTIONAL COEFFICIENTS."RB'ER$(10)"DIVISION BY ZERO IS NOT ALLOWED."ASUATION #1 BY -1. DOING THE SAME TO EQUATION #2 WOULD NEGATE THE CHANGE IN #1."Q.'ER$(7)"YOU HAVE ALREADY EQUALIZED THE COEFFICIENTS OF THE X OR Y VARIABLE. YOUR NEXT STEP IS TO ELIMINATE X OR Y BYADDING OR SUBTRACTING THE EQUATIONS."NR3'ENSTANTS YOU CHOSE TO MULTIPLY BY WILL NOT GIVE YOU EQUAL COEFFICIENTS FOR THE X OR Y VARIABLE.P$'ER$(5)"SINCE AT LEAST ONE SET OF COEFFICIENTS ARE ALREADY EQUALIZED, YOU SHOULD ADD OR SUBTRACT THE EQUATIONS."PQ)'ER$(6)"YOU ALREADY MULTIPLIED EQHE COEFFICIENTS OF X OR Y."O'ER$(2)"YOU MUST FIRST ADD OR SUBTRACT THE EQUATIONS IN ORDER TO ELIMINATE ONE OF THE TERMS CONTAINING X OR Y.O'ER$(3)"MULTIPLYING BY ZERO WILL MAKE EVERY TERM IN THE EQUATION EQUAL TO ZERO."bP'ER$(4)"THE CO N&FOUND2N&5400:"CONGRATULATIONS, ";N$;"! YOU HAVE"::"SOLVED THIS SYSTEM OF EQUATIONS."::1:34:"X = ";X0);X:2:34:"Y = ";Y0);Y::5300N&O'ER$(1)"YOU MUST MULTIPLY ONE OR BOTH OF THE EQUATIONS BY A VALUE THAT WILL EQUALIZE T%EX0:COCSV:VA$SV$:20000:CO(1)0Ģ7:6:16(RE$));RE$;" = ";CO(2):9800M&7:6:13(RE$)(((CO(1)))));RE$;OP$;(CO(1));" = ";CO(2)MH&CSV1CO(1)09900MR&5400:"NOW YOU CAN SOLVE THIS EQUATION FOR ";SV$;".":5300N\&COCSV:VS7:40000"THE MULTIPLICATION.":5300iL%ZM5:5400:CKV;" * ";KV;" = ";:900:C2$G$:CH$C2$:6400:BADC2$"1000"L%(C2$)CKVKVE3E31::"THAT IS INCORRECT."::CKV;" * ";KV;" = ";CKVKV:5300:9710L%CO(1)CKVKV:CO(2)SC:OP$" + ":CO(1)0OP$" - "NM")"0K%COSB:VA$"Y":KV$"X"EX2:20000:9640]K%CO0RE$"- "((CO),((CO))1):9630pK%RE$"+ "(CO)K%RE$RE$"("(Y)")"K%7:21(FT$)(RE$):FT$;" ";RE$;" = ";SCK%7:3:5700L%5400:"NOW SIMPLIFY THE LEFT SIDE BY PERFORMING":BB1:SCC1:G$"2"SAA2:SBB2:SCC2WJN%KVX:CKVSA:CSVSB:KV$"Y"KVY:CKVSB:CSVSAJ%5400:"FIRST, REWRITE EQUATION ";::G$;::", REPLACING"::KV$;" WITH ";KV;".":5300J%COSA:VA$"X":KV$"Y"EX0:20000:FT$RE$:9620K%FT$(CO)"("(X)V$:35000IT$I%5400:"TO SOLVE FOR ";SV$;", YOU MUST SUBSTITUTE"::"FOR ";KV$;" IN ONE OF THE ORIGINAL EQUATIONS.":5300I&%5400:"SUBSTITUTE FOR "KV$" IN EQUATION ";::1;::" OR ";::2;::"? ";I+%G$:G$"1"G$"2"9515:G$;:$JD%SAA1:S"RV$"X":COA5:A50RV$"Y":COB5WH"12:VA$RV$:EX0:20000:22(RE$):RE$;" = ";C5pH"CO1KV$RV$:35000{H"M13:H(# SOLV/VARH2#FOUND0SV$RV$:9100H<#SV$"X":KV$"X"SV$"Y"HF#9500H#VA$RV$:VS12:CO(1)0:CO(2)C5:40000 I#KV$R$C2$:6400:BAD8820JGj"(C2$)C5Ģ10:29((C5)):C5:5400:S60:8900Gt"E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:8800G~"C3;" + ";C4;" = ";C5:5300:V19:H1:NL4:5500:8800G"10:3:3);"Hκ"TO ISOLATE THE "VA$" TERM, YOU MUST"::"SUBTRACT ";CO(1);" FROM BOTH SIDES.":5300:42100f"YOU MUST SUBTRACT ";CO(1);" FROM BOTH SIDES.":5300:42100fVS:3:3);:VS2:3:5700fOP$" + ":CO(1)0OP$" - "DgVS2:16(LT$)((CO(1)))CO(1):5300:413002ehVS2:25:CO(2)CO(1);12)ZeVSVS2:CO(2)CO(2)CO(1):CO(1)0:ueCO(1)0ER17:5950:etZM5:5400:"VALUE TO SUBTRACT FROM BOTH SIDES: ";:900:CH$G$:6400:BAD42110ey(CH$)CO(1)42120\f~E2E21:5400:Y142115:S INCORRECT."::CO(1);" + ";CO(1);" = 0":5300:5400:41220\dVS2:6:16(LT$));LT$;dTZM5:5400:CO(2);" + ";CO(1);" = ";:900:CH$G$:6400:BADCH$""e^(CH$)CO(2)CO(1)E3E31::"THAT IS INCORRECT."::CO(2);" + ";CO(1);" = ";CO(2)T$;OP$;(CO(1));" + ";CO(1);" = ";CO(2);" + ";CO(1)c5400:"NOW YOU MUST SIMPLIFY BY COMBINING THE"::"CONSTANT TERMS ON EACH SIDE.":5300c5400cZM5:CO(1);" + ";CO(1);" = ";:900:CH$G$:6400:BADCH$"1"=d(CH$)0E3E31::"THAT ISOLATE THE "VA$" TERM, YOU MUST"::"ADD ";CO(1);" TO BOTH SIDES.":5300:41100b"YOU MUST ADD ";CO(1);" TO BOTH SIDES.":5300:41100bVS:3:3);:VS2:3:5700bOP$" + ":CO(1)0OP$" - "5cVS2:16(LT$)((CO(1)))(((CO(1)))):L(G1$):IN0IN440180ZZ:FR0:NU(CH$):DE1:43100jHNU$(CH$,ZZ1):DE$(CH$,ZZ1):FR1:CH$DE$:6400:BAD43130jRNU(NU$):DE(DE$):DE0NUNU:DEDEkW1);" = ";CO(2)CO(1):5300:42300AiPVS2:25:CO(2)CO(1);12)iiVSVS2:CO(2)CO(2)CO(1):CO(1)0:iZM5:5400:"MULTIPLY BOTH SIDES BY WHAT VALUE? ";:900:CH$G$iCH$""43000i (CH$)0ĭCH$"0"CH$"-0"CH$"+0"ER3:5950:43000 j31::"THAT IS INCORRECT."::CO(1);" - ";CO(1);" = 0":5300:5400:42220ihVS2:6:16(LT$));LT$;h.":9:10)"NAME: ";~NZZ0:ZH0:N$"":G1$""$QǾG1$:G1$(8)51025:XX((78)(79))1:X139:" ";::X223:39:X:" ";::X3911:24:X:" ";::X2321:1:X:" ";::}dâ7:6:"SIMULTANEOUS LINEAR EQUATIONS":16368,0}nâ10:5:"BY MARK BERMAN AND KEVIN VESSIO":12:10:"DESIGNED BY DON ROSS"~xâ15:9:"MICROCOMPUTER WORKS(CBY))):CAX;OP$;(CBY);" = ";CC@|8:3:3):10:3:5700b|10:22((CC)):CC;" = ";CC|X5400:"SINCE THE TWO SIDES OF THE EQUATION ARE"::"THE SAME, I KNOW THAT THE SOLUTION"::"CHECKS IN THIS EQUATION.":5300||P×: TITLE PG\}_Þ15:3:5700<{6VA$"("(X)")":COCA:EX0:20000:FT$RE$c{@VA$"("(Y)")":COCB:EX2:20000{J4:23:"?":5:21(FT$)(RE$):FT$;" ";RE$;" = ";CC{5:3:3):8:3:5700{OP$" + ":CBY0OP$" - "$|7:23:"?":8:19((CAX))(((CO(2)CH.5):VSVS2:+zȯ CHECK AN EQYzүCAA1:CBB1:CCC1:CH2CAA2:CBB2:CCC2qzܯV4:H1:NL12:5500z,5400:"I BEGIN BY SUBSTITUTING ";X;" FOR X AND ";Y::"FOR Y IN THE ORIGINAL EQUATION. NEXT, I":"WILL SIMPLIFY THE LEFT SIDE.":5300 {CO(2);" / ";CH;" = ";:900:C2$G$:CH$C2$:6400:BADC2$"1000"yu(C2$)(CO(2)CH.5)E3E31::"THAT IS INCORRECT."::CO(2);" / ";CH;" = ";(CO(2)CH.5):5300:44400yzVS2:25:(CO(2)CH.5);10)zԭCO(COCH.5):CO(1)(CO(1)CH.5):CO(2)1000"uxW(C2$)(CO(1)CH.5)E3E31::"THAT IS INCORRECT."::CO(1);" / ";CH;" = ";(CO(1)CH.5):5300:44370x\OP$" + ":CO(1)CH0OP$" - "xfVS2:1:18(C1$)((((CO(1)CH.5)))));C1$;OP$;((CO(1)CH.5)):VS2:3:5700?yp5400:6:16(C1$));C1$:44400iw4(C1$)((CO(1)))((CH))6Ė1:12(C1$)((CO(1)))((CH)));:44360w>6:8(C1$)((CO(1)))((CH)));wHC1$;" + (";CO(1);" / ";CH;")"xRZM5:5400:CO(1);" / ";CH;" = ";:900:C2$G$:CH$C2$:6400:BADC2$"T, ";CO;".":5300:44000+qCO(1)044250qVSVS2:VS2:1:13(LT$)(((CO(1))))((CH)));"(";LT$;1);:CO(1)0ĺ"+";:44230q"-";qƬ1);(CO(1));") / ";CH;" = ";CO(2);" / ";CH:44300 rڬVS2:19(LT$)((CH)):LT$;" / ";CH;" = ";CO($(21))40):5300:44000pD(CO(1)0CHCO)(CO(1)0(COCH(COCH)).00001(CO(1)CH(CO(1)CH)).00001(CO(2)CH(CO(2)CH)).00001)44200pNCO(1)0ER9:5950:qX5400:E2E21:"TO SOLVE FOR ";VA$;", YOU MUST DIVIDE BY"::"ITS COEFFICIENoZM5:5400:"DIVIDE BOTH SIDES BY WHAT VALUE: ";:900:G$""44000:CH$G$:CH$"1"CH$"+1"CH1:44020o嫰6400:BAD44120oCH(CH$):CH0ĭCH$"0"CH$"-0"CH$"+0"ER10:5950:44000o﫭CH044120pCH1İ5400:(ER$(21),40):(ER$(21),(ERpn(C2$)(CO(2)NUDE.5)E3E31::"THAT IS INCORRECT."::CH$;CO(2);" = ";(CO(2)NUDE.5):5300:43400nVS2:25:(CO(2)NUDE.5);14(((CO(2)NUDE.5))))nCO(CONUDE.5):CO(1)(CO(1)NUDE.5):CO(2)(CO(2)NUDE.5):VSVS2:jNCORRECT."::CH$;CO(1);" = ";(CO(1)NUDE.5):5300:43370cmtOP$" + ":CO(1)NUDE0OP$" - "m~VS2:1:18(C1$)((((CO(1)NUDE.5)))));C1$;OP$;((CO(1)NUDE.5)):VS2:3:5700mZM5:5400:CH$;CO(2);" = ";:900:C2$G$:C2$""43400(C1$)(CH$)((CO(1)))10Ė1:16(C1$)(CH$)((CO(1))));:43360olV6:11(C1$)(CH$)((CO(1))));l`C1$;" + ";OP$;CH$;CO(1);CL$ljZM5:5400:CH$;CO(1);" = ";:900:C2$G$:C2$""43370ZZ:FR0:NU(CH$):D5400:CO(2);" - ";CO(1);" = ";:900:CH$G$:6400:BAD42300eF(CH$)CO(2)CO(1)E3E31::"THAT IS INCORRECT."::CO(2);" - ";CO(1);" = ";CO(2)CO(1):5300:42300ePVS2:25:CO(2)CO(1);12)eVSVS2:CO(2)CO(2)CO(1):CO(1)0:)fZM5:5400::"CONSTANT TERMS ON EACH SIDE.":53002d⤰5400ydZM5:CO(1);" - ";CO(1);" = ";:900:CH$G$:6400:BADİ5400:42220d(CH$)0E3E31::"THAT IS INCORRECT."::CO(1);" - ";CO(1);" = 0":5300:5400:42220dVS2:6:16(LT$));LT$;!5400(:H!8:11:"+";X:R!17:1:"ADD THE EQUATIONS: TERM BY TERM."w:\!A5A3A4:B5B3B4:C5C3C4:f!10:3:5700:!19:1:VA$"X":EX0:COA3:20000:RE$;" + ";:COA4:20000:RE$;" = ";:"";C2$:C2$""8600=;!COA5:20000:C1$RE$ACT, YOU MUST CHANGE THE SIGNS"::"OF THE TERMS IN THE SUBTRAHEND.":5300:54009A4A4:B4B4:C4C4:DAA4:DBB4:DCC4:8:1:40):V8:H13:25000917:1:"NOW COMPLETE THE SUBTRACTION BY ADDING"::"THE RESULTING EQUATIONS.":5300:5400 :4!ADD E BOTTOM OF THE SCREEN WILL BE THE ":"FOLLOWING MENU:"ע15:4:"1. MULTIPLY/DIVIDE ";::"1";::" OR ";::"2";::" BY A":7:"CONSTANT":ז4:"2. ADD OR SUBTRACT EQUATIONS"::4:"3. SOLVE FOR VARIABLE X OR Y"װ5300ؗ::14:"MENU OPTIOE A UNIQUE SOLUTION SET ":"COMPRISED OF WHOLE NUMBERS."~Zע18:"USE THE ELIMINATION OF A VARIABLE":20:"METHOD TO SOLVE THE PROBLEMS."~dװ5300~ח:3:"FOR EACH PROBLEM, YOU WILL SEE TWO ":"EQUATIONS AT THE TOP OF THE SCREEN."7ע10:"AT TH"2"G1$"3"55030-}ֺG1$;:G1$"1"55100>}֭G1$"2"100O}׭G1$"3"740Z} ׫55030g}<ײ INSTR}Fח:N$",":4:"I WILL HELP YOU PRACTICE SOLVING SYSTEMS":"OF TWO SIMULTANEOUS LINEAR EQUATIONS ":"WITH TWO UNKNOWNS."8~Pע12:"ALL PROBLEMS HAV|eǺ(8)" "(8);:ZZ151022@|jN$(N$,(N$)1):ZZZZ1:51025P|ֲ MAIN MENU|TE(1)0:TE(2)0:TE(3)0::5:18::"MENU":|֢9:13:"1) INSTRUCTIONS"::13:"2) PROBLEMS"::13:"3) EXIT PROGRAM":17:6:"YOUR SELECTION: ";}־G1$:G1$"1"G1$AME: ";"{NZZ0:ZH0:N$"":G1$""b{QǾG1$:XX((78)(79))16:XX(XX):ZH(G1$):ZH13ZZ0ır{RǭZH851040{TǭZZ1051025{UǭZH65ZH12251025{VǭZH90ZH9751025{XǭZH90ZHZH32{[Ǻ(ZH);:ZZZZ1:N$N$(ZH):51025{`ǭZZ051025 KEVIN VESSIO":12:10:"DESIGNED BY DON ROSS"hzxâ15:9:"MICROCOMPUTER WORKSHOPS"::15:"COURSEWARE"zú:16:"(C) 1983":I14000::z8Dz GET NAME{LǗ:3:" PLEASE ENTER YOUR FIRST NAME (UP TO"::" TEN LETTERS) AND PRESS .":9:10)"N THE SOLUTION"::"CHECKS IN THIS EQUATION.":53008yIyP×: TITLE PGy_Þ:X139:" ";::X223:39:X:" ";::X3911:24:X:" ";::X2321:1:X:" ";::ydâ7:6:"SIMULTANEOUS LINEAR EQUATIONS":16368,0.znâ10:5:"BY MARK BERMAN AND3:5700(xOP$" + ":CBY0OP$" - "sx7:23:"?":8:19((CAX))(((CBY))):CAX;OP$;(CBY);" = ";CCx8:3:3):10:3:5700x10:22((CC)):CC;" = ";CC2yX5400:"SINCE THE TWO SIDES OF THE EQUATION ARE"::"THE SAME, I KNOW THAT Y IN THE ORIGINAL EQUATION. NEXT, I":"WILL SIMPLIFY THE LEFT SIDE.":5300\w15:3:5700w6VA$"("(X)")":COCA:EX0:20000:FT$RE$w@VA$"("(Y)")":COCB:EX2:20000wJ4:23:"?":5:21(FT$)(RE$):FT$;" ";RE$;" = ";CCx5:3:3):8:vzVS2:25:(CO(2)CH.5);10)hvԭCO(COCH.5):CO(1)(CO(1)CH.5):CO(2)(CO(2)CH.5):VSVS2:zvȯ CHECK AN EQvүCAA1:CBB1:CCC1:CH2CAA2:CBB2:CCC2vܯV4:H1:NL12:5500Lw,5400:"I BEGIN BY SUBSTITUTING ";X;" FOR X AND ";Y::"FOR(C1$)((((CO(1)CH.5)))));C1$;OP$;((CO(1)CH.5)):VS2:3:5700up5400:CO(2);" / ";CH;" = ";:900:C2$G$:CH$C2$:6400:BAD44400uu(C2$)(CO(2)CH.5)E3E31::"THAT IS INCORRECT."::CO(2);" / ";CH;" = ";(CO(2)CH.5):5300:44400!);" / ";CH;")"YtRZM5:5400:CO(1);" / ";CH;" = ";:900:C2$G$:CH$C2$:6400:BAD44370tW(C2$)(CO(1)CH.5)E3E31::"THAT IS INCORRECT."::CO(1);" / ";CH;" = ";(CO(1)CH.5):5300:44370t\OP$" + ":CO(1)CH0OP$" - "HufVS2:1:18 BE GRAPHED ONE AT A ":"TIME AND THE POINT OF INTERSECTION WILL ":"BE MARKED."[|ذ5300ع34,0::5:"AFTER EACH PROBLEM, I WILL GIVE YOU A ":"SUMMARY OF YOUR ERRORS. "آ11:"AFTER THE ERROR SUMMARY, YOU CAN QUIT OR":"GO ON TO THE NEXT PROBL300vhؗ:14:"WHEN YOU HAVE FOUND THE VALUES OF BOTH ":"VARIABLES, I WILL HELP YOU CHECK YOUR ":"ANSWER.":5300rع34,0::6:"AFTER CHECKING YOUR ANSWER, I WILL"::"SHOW YOU A GRAPHICAL SOLUTION TO"::"THE PROBLEM."::Qwغ"EACH EQUATION WILLRE NO WHOLE DIVISORS WHICH WILL ALLOW YOU TO GET EQUAL COEFFICIENTS FOR THE X OR Y VARIABLE."J`'ER$(13)"LEAVING BOTH EQUATIONS THE SAME DOES NOTHING TO HELP YOU FIND THE SOLUTION."Kj'ER$(14)"ADDING THESE EQUATIONS WILL NOT ELIMINATE ONE O(9)"YOUR DIVISOR WILL NOT DIVIDE EVENLY INTO ALL THE COEFFICIENTS. THIS WILL RESULT IN FRACTIONAL COEFFICIENTS."IB'ER$(10)"DIVISION BY ZERO IS NOT DEFINED."IL'ER$(11)"THE CONSTANTS YOU CHOSE TO DIVIDE BY "(ER$(4),41)^JV'ER$(12)"THERE AR$(7)"YOU HAVE ALREADY EQUALIZED THE COEFFICIENTS OF THE X OR Y VARIABLE. YOUR NEXT STEP IS TO ELIMINATE X OR Y BYADDING OR SUBTRACTING THE EQUATIONS."H3'ER$(8)"THE MULTIPLIER YOU HAVE CHOSEN WILL GIVEYOU FRACTIONS IN THE EQUATION."xI8'ER$ARIABLE.G$'ER$(5)"SINCE AT LEAST ONE SET OF COEFFICIENTS ARE ALREADY EQUAL, THE ONLY POSSIBLE MULTIPLICATION WOULD BE BY -1."G)'ER$(6)"YOU ALREADY MULTIPLIED EQUATION #1 BY -1. DOING THE SAME TO EQUATION #2 WOULD NEGATE THE CHANGE IN #1."H.'EIN ORDER TO ELIMINATE ONE OF THE TERMS CONTAINING X OR Y.F'ER$(3)"MULTIPLYING BY ZERO WILL MAKE EVERY TERM IN THE EQUATION EQUAL TO ZERO."G'ER$(4)"THE CONSTANTS YOU CHOSE TO MULTIPLY BY WILL NOT GIVE YOU EQUAL COEFFICIENTS FOR THE X OR Y VATIONS."::1:34:"X = ";X0);X:2:34:"Y = ";Y0);Y::5300HE&E'ER$(1)"YOU MUST MULTIPLY ONE OR BOTH OF THE EQUATIONS BY A VALUE THAT WILL EQUALIZE THE COEFFICIENTS OF X OR Y.":F'ER$(2)"YOU MUST FIRST ADD OR SUBTRACT THE EQUATIONS 13(RE$)(((CO(1)))));RE$;OP$;(CO(1));" = ";CO(2)ODH&CSV1CO(1)09900DR&5400:"NOW YOU CAN SOLVE THIS EQUATION FOR ";SV$;".":5300D\&COCSV:VS7:40000D&FOUND2BE&5400:"CONGRATULATIONS, ";N$;"! YOU HAVE"::"SOLVED THIS SYSTEM OF EQU6400:BAD9710lC%(C2$)CKVKVE3E31::"THAT IS INCORRECT."::CKV;" * ";KV;" = ";CKVKV:5300:9710C%CO(1)CKVKV:CO(2)SC:OP$" + ":CO(1)0OP$" - "C%EX0:COCSV:VA$SV$:20000:CO(1)0Ģ7:6:16(RE$));RE$;" = ";CO(2):98007D&7:6:(Y)")">B%EX2:20000:KV$"Y"(CO)1RE$(RE$,1)(RE$,3)mB%7:21(FT$)(RE$):FT$;" ";RE$;" = ";SC}B%7:3:5700B%5400:"NOW SIMPLIFY THE LEFT SIDE BY PERFORMING":"THE MULTIPLICATION.":5300C%5400:CKV;" * ";KV;" = ";:"";C2$:CH$C2$:CSVSB:KV$"Y"KVY:CKVSB:CSVSA~A%5400:"FIRST, REWRITE EQUATION ";::G$;::", REPLACING"::KV$;" WITH ";KV;".":5300A%(KV)1(CKV)19720A%COSA:VA$"X":KV$"X"VA$"("(X)")"B%EX0:20000:FT$RE$:COSB:VA$"Y":KV$"Y"VA$"("YOU MUST SUBSTITUTE"::"FOR ";KV$;" IN ONE OF THE ORIGINAL EQUATIONS.":5300@&%5400:"SUBSTITUTE IN EQUATION ";::1;::" OR ";::2;::"?"@0%V17:H32::5800::G$"1"G$"2"9510@D%SAA1:SBB1:SCC1:G$"2"SAA2:SBB2:SCC2"AN%KVX:CKVSA:000:22(RE$):RE$;" = ";C55?"CO1KV$RV$:35000@?"M13:X?(#SOLVE FOR VARIABLEs?2#FOUND0SV$RV$:9100?<#SV$"X":KV$"X"SV$"Y"?F#9500?#VA$RV$:VS12:CO(1)0:CO(2)C5:40000?#KV$RV$:35000?T$M@%5400:"TO SOLVE FOR ";SV$;", 5400:S60:8900v>t"E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:8800>~"C3;" + ";C4;" = ";C5:5300:V19:H1:NL4:5500:8800>"10:3:3);>"RV$"X":COA5:A50RV$"Y":COB5?"12:VA$RV$:EX0:2019:H1:NL4:5300:5500:8700w="COB3:20000:RE$;" + ";:COB4:20000:RE$;" = ";C1$:V19:H1:NL4:5300:5500:8700=`"10:22:" = ":19:1:C3;" + ";C4;" = ";:"";C2$:CH$C2$:6400:BADV19:H1:NL4:5500:8800>j"(C2$)C5Ģ10:29((C5)):C5:!19:1:VA$"Y":EX0:COB3:20000:RE$;" + ";:COB4:20000:RE$;" = ";:"";C2$:C2$""8700<"COB5:20000:C1$RE$:30000:CĢ10:18:EX2:20000:RE$:S60:V19:H1:NL4:5500:8800="E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V:30000:CĢ10:17(C1$):C1$:S60:V19:H1:NL4:5500:8700;!E3E31::"SORRY, THAT IS INCORRECT.":S6S61:S61ĺ"TRY AGAIN.":V19:H1:NL4:5300:5500:8600;!COA3:20000:RE$;" + ";:COA4:20000:RE$;" = ";C1$:V19:H1:NL4:5300:5500:8600\QPCO0RE$"+ "(CO)VA$:YQPCO9RE$(CO)VA$:sQPRE$"- "(CO)VA$:QaPRINT EQUATION ROUTINEQaPASS COEFFICIENTS OFQaX, Y IN DA, DBQaPASS CONSTANT IN DCQaV:HRaVA$"X":CODA:EX1:20000:D IN RE$P4NEX20300,206005PNCO1RE$"-"VA$:IPNCO1RE$VA$:]PNRE$(CO)VA$:xPLOCO1RE$" -"VA$:PVOCO1RE$" "VA$:P`ORE$(CO)VA$PjO(RE$)4RE$" "RE$:20330PtOPxPCO1RE$"- "VA$:QPCO1RE$"+ "VA$:LL GET IT."@OT)ME$(8)"DON'T BE DISCOURAGED. YOU'LL DO BETTER."FO*^O NCONVERSION ROUTINE}O!NPASS VARIABLE NAME IN VA$O"NPASS COEFFICIENT IN COO#NTO FORCE LENGTH TO AT LEAST 3, SET EX=1O$NSET EX=2 FOR SECOND TERM FORMATP%NVALUE RETURNEOO BAD YOUR TEACHER CAN'T SEE THIS."PN")ME$(3)"WELL, WE CAN'T ALL BE PERFECT."N,)ME$(4)"OKAY "N$", THAT WAS A GOOD TRY."N6)ME$(5)"YOU ALMOST MADE IT ON THAT ONE."N@)ME$(6)"THESE PROBLEMS ARE NOT SO EASY." OJ)ME$(7)"KEEP TRYING, "N$". YOU'E ABSOLUTE VALUE IS GREATER THAN 1 WILL NOT HELP TOSIMPLIFY THE EQUATION."M'ER$(20)"MULTIPLYING BOTH SIDES BY ONE WILL HAVE NO EFFECT ON THE EQUATION."M)ME$(0)"VERY IMPRESSIVE, "N$M)ME$(1)"I SEE YOU'VE BEEN DOING YOUR HOMEWORK."$N)ME$(2)"TT BY USING MULTIPLICATION OR DIVISION."L'ER$(18)"BEFORE YOU CAN ELIMINATE THE COEFFICIENTOF THE VARIABLE, YOU MUST USE ADDITION OR SUBTRACTION TO ELIMINATE THE CONSTANTTERM ON THE LEFT SIDE OF THE EQUATION."KM'ER$(19)"MULTIPLYING BY A NUMBER WHOSF THE VARIABLES."VKt'ER$(15)"SUBTRACTING THESE EQUATIONS WILL NOT "(ER$(14),41)K~'ER$(16)"YOU'RE ALMOST DONE. THE NEXT STEP IS TOSOLVE FOR EITHER 'X' OR 'Y'.")L'ER$(17)"TO SOLVE FOR THE VALUE OF THE VARIABLE, YOU MUST ELIMINATE ITS COEFFICIENNUDE.5))))]jCO(CONUDE.5):CO(1)(CO(1)NUDE.5):CO(2)(CO(2)NUDE.5):VSVS2:j૰5400:"DIVIDE BOTH SIDES BY WHAT VALUE: ";CH$:6400:BAD44000jCH(CH$):CH0ER10:5950:44000EkD(CO(1)0CHCO)(CO(1)0(COCH(COCH)).00001;C1$;OP$;((CO(1)NUDE.5)):VS2:3:5700^i5400:CH$;CO(2);" = ";:"";C2$:C2$""43400i(C2$)(CO(2)NUDE.5)E3E31::"THAT IS INCORRECT."::CH$;CO(2);" = ";(CO(2)NUDE.5):5300:43400 jVS2:25:(CO(2)NUDE.5);14(((CO(2)$3hj5400:CH$;CO(1);" = ";:"";C2$:C2$""43370ho(C2$)(CO(1)NUDE.5)E3E31::"THAT IS INCORRECT."::CH$;CO(1);" = ";(CO(1)NUDE.5):5300:43370htOP$" + ":CO(1)NUDE0OP$" - ",i~VS2:1:18(C1$)((((CO(1)NUDE.5))))) = ";C1$:5300:43310Cg8VS2:CO(1)0Ė6:16(C1$));C1$:43400kgBOP$"(":CL$")":FROP$"[":CL$"]"gL(C1$)(CH$)((CO(1)))10Ė1:16(C1$)(CH$)((CO(1))));:43360gV6:11(C1$)(CH$)((CO(1))));h`C1$;" + ";OP$;CH$;CO(1);CL5700bf$5400:"NOW YOU MUST SIMPLIFY BY PERFORMING THE"::"MULTIPLICATION ON EACH SIDE.":5300f.5400:CH$;LT$;" = ";:"";C2$:C2$""43310g3T1CO:CO(CONUDE.5):EX0:20000:C1$RE$:COT1:30000:CE3E31::"THAT IS INCORRECT."::CH$;LT$;"E)") * "eʨCO(1)043250eԨVSVS2:VS2:3:36);:17(CH$)(LT$)(((CO(1)))):CH$;"(";LT$;:CO(1)0ĺ" + ";:43240eި" - ";e診(CO(1));") = ";CH$;CO(2):43300eVS2:22(CH$)(LT$):CH$;LT$;" = ";CH$;CO(2)fVS:3:3):VS2:3:NUER20:5950:!dpER8:5950:dz5400:E2E21:"TO ELIMINATE THE ";CO;", YOU MUST"::"MULTIPLY BY ITS RECIPROCAL, ";:CO1ĺ"-1.":43160dCO0ĺ"-1/";CO;".":43160d"1/";CO;"."d5300:43000 eCH$(NU)" * ":FRCH$"("(NU)"/"(D10:5950:43000c\(DENU1CO(1)0)((DENUCO).00001CO(1)0)(CO(1)0DE(NU)(CONUDE(CONUDE)).00001(CO(1)NUDE(CO(1)NUDE)).00001(CO(2)NUDE(CO(2)NUDE)).00001)43200cfCO(1)043130ckDE(NU)ER19:5950:dmDE):ZZ$(CH$,ZZ,1):ZZ$"/"43080ab4ZZ$"-"ZZ$"+"ZZ$" "ZZ$"."(ZZ$"0"ZZ$"9")43000b>ZZ:FR0:NU(CH$):DE1:43100bHNU$(CH$,ZZ1):DE$(CH$,ZZ1):FR1:CH$DE$:6400:BAD43000bRNU(NU$):DE(DE$):DE0NUNU:DEDEcWDE0ER1);12)/aVSVS2:CO(2)CO(2)CO(1):CO(1)0:Ya5400:"MULTIPLY BOTH SIDES BY: ";CH$kaCH$""43000a (CH$)0ER3:5950:43000a(CH$)543000:REJECT ATTEMPTS AT REPEATING DECIMALSa SCAN STRING TO CHECK FOR FRACTION b*ZZ1(CH$O(1);" = 0":5300:5400:42220=`VS2:6:16(LT$));LT$;z`<5400:CO(2);" - ";CO(1);" = ";:"";CH$:6400:BAD42300`F(CH$)CO(2)CO(1)E3E31::"THAT IS INCORRECT."::CO(2);" - ";CO(1);" = ";CO(2)CO(1):5300:42300aPVS2:25:CO(2)CO(O(1);" = ";CO(2);" - ";CO(1)x_ؤ5400:"NOW YOU MUST SIMPLIFY BY COMBINING THE"::"CONSTANT TERMS ON EACH SIDE.":5300_⤰5400_줺CO(1);" - ";CO(1);" = ";:"";CH$:6400:BADİ5400:42220`(CH$)0E3E31::"THAT IS INCORRECT."::CO(1);" - ";C$)CO(1)E2E21:5400:"TO ELIMINATE THE ";CO(1);", YOU MUST"::"SUBTRACT ";CO(1);" FROM BOTH SIDES.":5300:42100^VS:3:3);:VS2:3:5700^OP$" + ":CO(1)0OP$" - "_VS2:16(LT$)((CO(1)))(((CO(1)))):LT$;OP$;(CO(1));" - ";C::"THAT IS INCORRECT."::CO(2);" + ";CO(1);" = ";CO(2)CO(1):5300:41300m]hVS2:25:CO(2)CO(1);12)]VSVS2:CO(2)CO(2)CO(1):CO(1)0:]CO(1)0ER17:5950:]t5400:"VALUE TO SUBTRACT FROM BOTH SIDES: ";CH$:6400:BAD42100u^~(CH ";:"";CH$:6400:BADİ5400:41220\(CH$)0E3E31::"THAT IS INCORRECT."::CO(1);" + ";CO(1);" = 0":5300:5400:41220\VS2:6:16(LT$));LT$;\T5400:CO(2);" + ";CO(1);" = ";:"";CH$:6400:BAD41300M]^(CH$)CO(2)CO(1)E3E31 ":CO(1)0OP$" - "~[VS2:16(LT$)((CO(1)))(((CO(1)))):LT$;OP$;(CO(1));" + ";CO(1);" = ";CO(2);" + ";CO(1)[5400:"NOW YOU MUST SIMPLIFY BY COMBINING THE"::"CONSTANT TERMS ON EACH SIDE.":5300[5400#\CO(1);" + ";CO(1);" =4Xzؖ4:"1. MULTIPLY/DIVIDE ";::"1";::" OR ";::"2";::" BY A":7:"CONSTANT":zؖ4:"2. ADD OR SUBTRACT EQUATIONS"::4:"3. SOLVE FOR VARIABLE "(34)"X"(34)" OR "(34)"Y"(34)c{ آ13:34,9:::::"USE ";::"OPTION #1";::" TO MULTIPLY OHE ":"FOLLOWING MENU:"qyע15:4:"1. MULTIPLY/DIVIDE ";::"1";::" OR ";::"2";::" BY A":7:"CONSTANT":yז4:"2. ADD OR SUBTRACT EQUATIONS"::4:"3. SOLVE FOR VARIABLE "(34)"X"(34)" OR "(34)"Y"(34)yװ5300zؗ::14:"MENU OPTIONS"::RISED OF WHOLE NUMBERS."jxZע18:"USE THE ELIMINATION OF A VARIABLE":20:"METHOD TO SOLVE THE PROBLEMS."txdװ5300xח:3:"FOR EACH PROBLEM, YOU WILL SEE TWO ":"EQUATIONS AT THE TOP OF THE SCREEN."yע10:"AT THE BOTTOM OF THE SCREEN WILL BE T89ZZ12155050.w׹16368,0:ZZ78ZZ110ıGw<ײPRINT INSTRUCTIONS wFח:N$",":4:"I WILL HELP YOU PRACTICE SOLVING SYSTEMS":"OF TWO SIMULTANEOUS LINEAR EQUATIONS ":"WITH TWO UNKNOWNS."xPע12:"ALL PROBLEMS HAVE A UNIQUE SOLUTION SET ":"COMPQv`ǭ(N$)10N$(N$,10)::::"I'LL CALL YOU ";N$;" FOR SHORT.":ZZ12000:ZZWvjDZrvֲGIVE INSTRUCTIONS, IFvֲWANTED.v֗v֢8:"HI, "N$"!":10:"DO YOU WANT INSTRUCTIONS (Y/N)?"v׹16368,0w ZZ(1):ZZ(16384)128:ZZ78ZZ110ZZK BERMAN"-uxú:9:"MICROCOMPUTER WORKSHOPS"Cuú:15:"(C) 1983"VuÁI14000:I:nu8DzGET STUDENT'S NAMEtuBǗuLǢ8:"PLEASE ENTER YOUR FIRST NAME (UP TO TEN ":"CHARACTERS). THEN PRESS ";::"RETURN";::".":13:"NAME: ";uVDŽ"";N$:N$""51010N.":5300t'tPòPRINT A TITLE PAGE-tZ×t_Þ:X139:" ";::X223:39:X:" ";::X3911:24:X:" ";::X2321:1:X:" ";::tdâ5:16:"SOLVING":8:6:"SIMULTANEOUS LINEAR EQUATIONS" unâ12:15:"WRITTEN BY":15:9:"DON ROSS AND MARJs7:23:"?":8:19((CAX))(((CBY))):CAX;OP$;(CBY);" = ";CCfs8:3:3):10:3:5700s10:22((CC)):CC;" = ";CC tX5400:"SINCE THE TWO SIDES OF THE EQUATION ARE"::"THE SAME, I KNOW THAT THE SOLUTION"::"CHECKS IN THIS EQUATIOI":"SIMPLIFY THE LEFT SIDE.":53003r15:3:5700br6VA$"("(X)")":COCA:EX0:20000:FT$RE$r@VA$"("(Y)")":COCB:EX2:20000rJ4:23:"?":5:21(FT$)(RE$):FT$;" ";RE$;" = ";CCr5:3:3):8:3:5700rOP$" + ":CBY0OP$" - "2:qȯCHECK AN EQUATION.1qɯSET CH TO NUMBERHqʯOF EQUATION TO BEVq˯CHECKED.qүCAA1:CBB1:CCC1:CH2CAA2:CBB2:CCC2qܯV4:H1:NL12:5500#r,5400:"I BEGIN BY SUBSTITUTING ";X;" FOR X AND ";Y::"FOR Y IN THE ORIGINAL EQUATION. NEXT, H;" = ";:"";C2$:CH$C2$:6400:BAD44400pu(C2$)(CO(2)CH.5)E3E31::"THAT IS INCORRECT."::CO(2);" / ";CH;" = ";(CO(2)CH.5):5300:44400pzVS2:25:(CO(2)CH.5);10)qԭCO(COCH.5):CO(1)(CO(1)CH.5):CO(2)(CO(2)CH.5):VSVSC2$)(CO(1)CH.5)E3E31::"THAT IS INCORRECT."::CO(1);" / ";CH;" = ";(CO(1)CH.5):5300:44370o\OP$" + ":CO(1)CH0OP$" - "ofVS2:1:18(C1$)((((CO(1)CH.5)))));C1$;OP$;((CO(1)CH.5)):VS2:3:5700)pp5400:CO(2);" / ";C6:16(C1$));C1$:44400jn4(C1$)((CO(1)))((CH))6Ė1:12(C1$)((CO(1)))((CH)));:44360n>6:8(C1$)((CO(1)))((CH)));nHC1$;" + (";CO(1);" / ";CH;")"nR5400:CO(1);" / ";CH;" = ";:"";C2$:CH$C2$:6400:BAD44370hoW( PERFORMING THE"::"DIVISION ON EACH SIDE.":5300gm5400:LT$;" / ";CH;" = ";:"";C2$:C2$""44310mT1CO:CO(COCH.5):EX0:20000:C1$RE$:COT1:30000:CE3E31::"THAT IS INCORRECT."::LT$;" / ";CH;" = ";C1$:5300:44310n VS2:CO(1)0((CO(1))))((CH)));"(";LT$;1);:CO(1)0ĺ"+";:44230Cl"-";{lƬ1);(CO(1));") / ";CH;" = ";CO(2);" / ";CH:44300lڬVS2:19(LT$)((CH)):LT$;" / ";CH;" = ";CO(2);" / ";CHl䬢VS:3:3):VS2:3:57002m 5400:"NOW YOU MUST SIMPLIFY BY(CO(1)CH(CO(1)CH)).00001(CO(2)CH(CO(2)CH)).00001)44200`kNCO(1)0ER9:5950:kX5400:E2E21:"TO SOLVE FOR ";VA$;", YOU MUST DIVIDE BY"::"ITS COEFFICIENT, ";CO;".":5300:44000kCO(1)0442509lVSVS2:VS2:1:13(LT$)(E A UNIQUE SOLUTION SET ":"COMPRISED OF WHOLE NUMBERS."~Zע18:"USE THE ELIMINATION OF A VARIABLE":20:"METHOD TO SOLVE THE PROBLEMS."~dװ5300~ח:3:"FOR EACH PROBLEM, YOU WILL SEE TWO ":"EQUATIONS AT THE TOP OF THE SCREEN."7ע10:"AT TH"2"G1$"3"55030-}ֺG1$;:G1$"1"55100>}֭G1$"2"100O}׭G1$"3"740Z} ׫55030g}<ײ INSTR}Fח:N$",":4:"I WILL HELP YOU PRACTICE SOLVING SYSTEMS":"OF TWO SIMULTANEOUS LINEAR EQUATIONS ":"WITH TWO UNKNOWNS."8~Pע12:"ALL PROBLEMS HAV|eǺ(8)" "(8);:ZZ151022@|jN$(N$,(N$)1):ZZZZ1:51025P|ֲ MAIN MENU|TE(1)0:TE(2)0:TE(3)0::5:18::"MENU":|֢9:13:"1) INSTRUCTIONS"::13:"2) PROBLEMS"::13:"3) EXIT PROGRAM":17:6:"YOUR SELECTION: ";}־G1$:G1$"1"G1$AME: ";"{NZZ0:ZH0:N$"":G1$""b{QǾG1$:XX((78)(79))16:XX(XX):ZH(G1$):ZH13ZZ0ır{RǭZH851040{TǭZZ1051025{UǭZH65ZH12251025{VǭZH90ZH9751025{XǭZH90ZHZH32{[Ǻ(ZH);:ZZZZ1:N$N$(ZH):51025{`ǭZZ051025 KEVIN VESSIO":12:10:"DESIGNED BY DON ROSS"hzxâ15:9:"MICROCOMPUTER WORKSHOPS"::15:"COURSEWARE"zú:16:"(C) 1983":I14000::z8Dz GET NAME{LǗ:3:" PLEASE ENTER YOUR FIRST NAME (UP TO"::" TEN LETTERS) AND PRESS .":9:10)"N THE SOLUTION"::"CHECKS IN THIS EQUATION.":53008yIyP×: TITLE PGy_Þ:X139:" ";::X223:39:X:" ";::X3911:24:X:" ";::X2321:1:X:" ";::ydâ7:6:"SIMULTANEOUS LINEAR EQUATIONS":16368,0.znâ10:5:"BY MARK BERMAN AND3:5700(xOP$" + ":CBY0OP$" - "sx7:23:"?":8:19((CAX))(((CBY))):CAX;OP$;(CBY);" = ";CCx8:3:3):10:3:5700x10:22((CC)):CC;" = ";CC2yX5400:"SINCE THE TWO SIDES OF THE EQUATION ARE"::"THE SAME, I KNOW THAT Y IN THE ORIGINAL EQUATION. NEXT, I":"WILL SIMPLIFY THE LEFT SIDE.":5300\w15:3:5700w6VA$"("(X)")":COCA:EX0:20000:FT$RE$w@VA$"("(Y)")":COCB:EX2:20000wJ4:23:"?":5:21(FT$)(RE$):FT$;" ";RE$;" = ";CCx5:3:3):8:vzVS2:25:(CO(2)CH.5);10)hvԭCO(COCH.5):CO(1)(CO(1)CH.5):CO(2)(CO(2)CH.5):VSVS2:zvȯ CHECK AN EQvүCAA1:CBB1:CCC1:CH2CAA2:CBB2:CCC2vܯV4:H1:NL12:5500Lw,5400:"I BEGIN BY SUBSTITUTING ";X;" FOR X AND ";Y::"FOR0}ZZ66:PL(1,1)ZZ:PL(1,2).3:PL(2,1)ZZ:PL(2,2).3:62000:PL(1,1).3:PL(1,2)ZZ:PL(2,1).3:PL(2,2)ZZ:62000:ZZtPL(1,1)7.5:PL(1,2).5:62500:5~PL(1,1).5:PL(1,2)7.5:62500:6PL(1,1)51SIZEASPECT:PL(1,2)1.5:62500:3#PL24:13:"PRESS <0>: ";:G$""8<G$:G$"0"1340:G$;F10:23:"= 0";:1:" ";:34,11::20:12:"4Y = 0":14:15:"WELL DONE!"::9:"NOW WE MUST SOLVE FOR Y.":100H34,12::200:24:13:"PRESS <3>: ";JG$:G$"3"1354:G$;-P34,12OUR ERRORS. "Wآ12:"AT THIS POINT, YOU CAN QUIT OR GO ON TO"::"THE NEXT PROBLEM."آ18:"WHEN YOU FINISH ALL THE PROBLEMS, I WILL":"SUMMARIZE YOUR TOTAL ERRORS."ذ53000ٗ:12:16(N$)2:"GOOD LUCK, ";N$;".":ZZ12000:ZZ:ZILL SHOW YOU A ":"GRAPHICAL SOLUTION TO THE PROBLEM."::~wغ::"EACH EQUATION WILL BE GRAPHED ONE AT A ":"TIME, AND THE POINT OF INTERSECTION WILL":"BE MARKED."~|ذ5300 ع34,0::5:"AFTER EACH PROBLEM, I WILL GIVE YOU A ":"SUMMARY OF YEN YOU FINISH WITH THAT VARIABLE, USE ":"OPTION #3 AGAIN TO SOLVE FOR THE OTHER ":"VARIABLE.":5300}hؗ:14:"WHEN YOU HAVE FOUND THE VALUES OF BOTH ":"VARIABLES, I WILL HELP YOU CHECK YOUR ":"ANSWER.":5300>~rع34,0::6:"AFTER THE CHECKS, I W"EQUATIONS IN ORDER TO ELIMINATE ONE OF ":"THE VARIABLES."|غ:"REMEMBER: FIRST EQUALIZE THE COEFFI- ":"CIENTS OF AT LEAST ONE OF THE VARIABLES."|"ذ5300|,ؗ:13:"USE ";::"OPTION #3";::" TO SOLVE FOR THE REMAINING":"VARIABLE."f}1غ:"WHR DIVIDE THE ":"ORIGINAL EQUATIONS BY A CONSTANT AND"::"EQUALIZE THE COEFFICIENTS OF ONE OF THE"w{ غ:"VARIABLES."{آ21:"REMEMBER: TO MULTIPLY, USE THE "(34)"*."(34){ذ5300<|ؗ:13:"USE ";::"OPTION #2";::" TO ADD OR SUBTRACT ":NCORRECT."::CH$;CO(1);" = ";(CO(1)NUDE.5):5300:43370chtOP$" + ":CO(1)NUDE0OP$" - "h~VS2:1:18(C1$)((((CO(1)NUDE.5)))));C1$;OP$;((CO(1)NUDE.5)):VS2:3:5700h5400:CH$;CO(2);" = ";:"";C2$:C2$""43400gi(C2"]"PgL(C1$)(CH$)((CO(1)))10Ė1:16(C1$)(CH$)((CO(1))));:43360xgV6:11(C1$)(CH$)((CO(1))));g`C1$;" + ";OP$;CH$;CO(1);CL$gj5400:CH$;CO(1);" = ";:"";C2$:C2$""43370: ";dG$:G$"4"1380:G$;kn:::"WE MUST DEM."_آ17:"WHEN YOU FINISH A SET OF PROBLEMS, I"::"WILL GIVE YOU A TOTAL ERROR ANALYSIS."iذ53000ٗ:10:7:"WOULD YOU LIKE TO SEE A"::7:"SAMPLE PROBLEM (Y OR N)? ";:G$""މ:پG$:G$"N"G$"n"ĺ"N";:55000D٭G$"Y"G$"y"55610 Nٺ"QG1$:G1$(8)910:ZH(G1$):ZH13Ĵ(G$,1)"-"(G$,1)"+"(G$,1)"/"910G1$(13)ĭ(G$,2)"/1"G$(G$,(G$)2):G1$(13)G$""ıG1$"-"G1$"+"ĭZZ0910ZH8940W91ZZ0ZH27G$"": ZZZMG$"0"G$"-0"47731(43626):b G$(ZZ):3(G$));G$;:34:ZZZZP%:G$(ZZ):ZZ(ZZ)G$G$".00":820*ZZ1(G$):(G$,ZZ,1)"."Ă/G$(G$,ZZ2):(G$,1)"."G$"0"G$0(G$,(G$)1,1)"."G$G$"0"46(G$));G$:G1$"":G$"":ZZ0:ZH0";:P%1ĺ".":730"S."-5300:55000:9:T$"THANK YOU, "N$".":(40(T$))2)T$:" I HOPE YOU ENJOYED THIS PROGRAM.":" PRESS RETURN TO REBOOT THE DISK.":20:16368,0P$:P$(13)750:(42204)238(42205)16(42206)192ČLIMINATING A VARIABLE .... ";:ZZTE(1):800:b"SOLVING LINEAR EQUATIONS .. ";:ZZTE(2):800:"COMPUTATIONAL ............. ";:ZZTE(3):800::"GRAND TOTAL ............... ";:ZZTE(1)TE(2)TE(3):800::7)"YOU COMPLETED "P%" PROBLEM;>16384,128:ZZ(16384)128:16368,0:ZZ81ZZ113700NZZ13660W200:11:"TOTAL ERROR ANALYSIS":::33)"AVERAGE";:35)"PER":" ERROR NUMBER PROBLEM";" ----- ------ -------";:-"E3((E1E2E3)))E1E2E3Pv19:ME$(3((E1E2E30)(E1E2E31))(3(1)))TE(1)TE(1)E1:TE(2)TE(2)E2:TE(3)TE(3)E3:ZZ(0):P%N%İ5300:70022:" PRESS ";::"RETURN";::" FOR NEXT PROBLEM."::12:"PRESS ";::"Q";::" TO QUIT."]" ----- ------":b"ELIMINATING A VARIABLE ........";3((E1)))E1::"SOLVING LINEAR EQUATIONS ......";3((E2)))E2:q"COMPUTATIONAL .................";3((E3)))E3:31);"----"::"TOTAL .........................";.":5300D5400:"WE CAN ALSO CHECK THE SOLUTION BY"::"GRAPHING THE EQUATIONS.":24:12:"ONE MOMENT, PLEASE.";:22:34,24::55700:(4);"RUN GRAPH"X16368,0::7:"ERROR SUMMARY FOR PROBLEM #";P%::::" ERROR NUMBER"+400:"NOW, I'LL CHECK YOUR ANSWER. FIRST,"::"I'LL CHECK EQUATION ";::1;::".":CH1:5300:45000 05400:"NEXT, I'LL CHECK EQUATION ";::2;::".":CH2:5300:45000:5400:"SINCE THE SOLUTION CHECKS IN BOTH"::"EQUATIONS, WE KNOW IT'S CORRECT hC1A1XB1Y:C2A2XB2Y0 |::"SOLVE":A 1:7::"1"R 2:7:"2": V1:H13:DAA1:DBB1:DCC1:25000:V2:H13:DAA2:DBB2:DCC2:25000 V3:5200 V16:5200 ER0:5100 5600:ER500 ER0:7000 FOUND2500e &5 P%P%1:E10:E20:E30:R107 @A1R(R):A10320N JA2R(R):A20330e TB1R(R):B10340| YB2R(R):B20345 \M11:MD0:FOUND0 ^S10:(A1)(A2)(B1)(B2)S11:M12 `A1B1A2B2320 cR10:XR(R):YR(R) eX0Y0355OGRAM WILL HELP YOU PRACTICE"::"SOLVING SIMULTANEOUS LINEAR EQUATIONS.":5300Z Z55000 d:3:N$",":::"YOU MAY TRY UP TO 9 PROBLEMS."::"HOW MANY WOULD YOU LIKE? ";:G1$"" nG1$:G1$(8)110:N%(G1$):N%0110:G1$:P%0 DO N% PROBLEMS <ZZ0:ZZ$"":Z$"":Z1$"":C1$"":C2$"":CO0:CH$"":VA$"":RE$""d =(779)1İ55800:10000:600 >N$"":ZZ(769):ZZ080:ZH769 @ZZ(ZH):ZZ0N$N$(ZZ):ZHZH1:64 B10000:90 P50000:51000:10000O R:4:"HI, "N$"!":::"THIS PR33,40:34,0:16384,0/ SIMULTANEOUSG LINEAR EQUATIONS _ COPYRIGHT (C) 1983}MICROCOMPUTER WORKSHOPS PORTCHESTER, NY LAST UPDATE:11/30/84 BY: KEVIN VESSIOAR$"-->":R(X)((1)X1)X27ER$(22),ME$(8)CIVIDE BY THE COEFFICIENT OF Y.":15:L$;:"DIVIDE BOTH SIDES BY WHAT VALUE? ":24:13:"PRESS <4>: ";:G$""xG$:G$"4"1400:G$;::16:"4Y / 4 = 0 / 4"::"NOW YOU MUST PERFORM THE DIVISION ON"::"EACH SIDE.":100:34,15:$15:L$:"4Y /! ! ! ! ! !!!!!!!!!"""                                   +";)VA$"Y":COB2:60150:VA$"":COC2;60150:60180]VA$""ĺ"="3((CO)))CO;:VA$"X"60157:CO1ĺ" "VA$;:CO1ĺ"- "VA$;:CO0ĺCO;VA$;:"-";(CO);VA$;:CO1ĺ" "VA$;:CO1ĺ" -"VA$;: 2((CO)":CODA:EX1:20000:RE$;" ";GaVA$"Y":CODB:EX2:20000:RE$;" = ";]a4((DC)));DC;cao` GRAPHz610001:29:VA$"X":COA1:60150:B10ĺ"+";VA$"Y":COB1:60150:VA$"":COC1601502:29:VA$"X":COA2:60150:B20ĺ"RE$(CO)VA$. jO(RE$)4RE$" "RE$:203304 tOO xPCO1RE$"- "VA$:i PCO1RE$"+ "VA$: PCO9RE$"+"(CO)VA$: PCO0RE$"+ "(CO)VA$: PCO9RE$(CO)VA$: PRE$"- "(CO)VA$: a PRINT EQ aV:HaVA$"X28(792):C2128(793):DA128(794):DB128(795):DC128(796):X128(797):Y128(798):q N CONV ROUTINE 4NEX20300,20600 NCO1RE$"-"VA$: NCO1RE$VA$: NRE$(CO)VA$: LOCO1RE$" -"VA$: VOCO1RE$" "VA$: `O798,128Y:$ > RESTORE VARIABLESW >ZZ768778:ZH(ZZ):ZH016010:N$N$(ZH): >RC%(779):P%(780):N%(781):E1(782):E2(783):E3(784):TE(1)(785):TE(2)(786):TE(3)(787):A1128(788):A2128(789)] >B1128(790):B2128(791):C11ZZ768:ZH1(N$):ZZ,((N$,ZH,1)):ZZZZ1::ZZ,0:779,1:780,P%:781,N%:782,E1:783,E2:784,E3:785,TE(1):786,TE(2):787,TE(3):788,128A1:789,128A2:790,128B1 :791,128B2:792,128C1:793,128C2:794,128DA:795,128DB:796,128DC:797,128X:141Ĺ16368,0:53203 16368,0:24:7:30);:M  ERASE BOT OF SCRl "34,20:21:(16);:34,0: 'START UP HRCG 'OLDHI(0):OLDHI(115)(116)256 $'OLDHI3000 .'(4);"BLOAD RBOOT":520:ADRS(0),"HRCG": : SAVE VARIABLES :16000:10000: (4);"BLOAD SHAPES":232,0:233,3Q(7);:34,0:5300hSIZE10:ASPECT1.3:16302,0:ADRS3d60000:MAIN BODYRETURN16368,0:24:9:"PRESS ";::" RETURN";::" TO CONTINUE."; 16384,128:(16384)""""""""    G$"-"1010 ZH13G$""ıPG1$"-"ZG0ZGZG1:G1$;:G$G$G1$:1010fZH49ZH571010(G$,1)"-"ZG11010(G$,1)"-"ZG01010G$G$G1$:ZGZG1:G1$;:1010ZG01010(8)" "(8);:ZG11000 ZGZG1:G$(G 5"::21:"X = 5":14:"WE HAVE SOLVED THIS SYSTEM OF EQUATIONS!":100T34,6::21:"X = 5":10:"IF THIS WERE AN ACTUAL PROBLEM, I WOULD"::"CHECK YOUR ANSWER BY SUBSTITUTING FOR"::"X AND Y IN EACH EQUATION.":100`^34,9::"FINALLY, I WOULD OF THE EQUATIONS. LET'S"::"SUBSTITUTE FOR Y IN THE FIRST EQUATION.":15:L$6"SUBSTITUTE FOR Y IN EQUATION ";::"1";::" OR ";::"2";::"? ":24:13:"PRESS <1>: ";:G$""@G$:G$"1"1600::G$;:HJ:14:"X + 5(0) = 5"::17:"X + 0 = UE OF Y.":10034,3:::21:"Y = 0":10:"SINCE WE HAVE FOUND THE VALUE OF Y, OUR"::"NEXT STEP IS TO SOLVE FOR X.":200:24:13:"PRESS <3>: ";:G$"""G$:G$"3"1570:G$;N,34,6:::"TO SOLVE FOR X, YOU MUST SUBSTITUTE"::"FOR Y IN ONE 4 = ":24:13:"PRESS : ";:G$""HG$:G$"Y"G$"y"1520:"Y";14:16:" Y";:17:1:15);:1:"0 / 4 = ":400:24:13:"PRESS <0>: ";:G$""G$:G$"0"1540:G$;14:26:" ";:26:"0";:34,15::17:8:"NOW WE KNOW THE VAL51(G$):(G$,X5,1)G1$910:@ZZZZ1:G1$;:G$G$G1$:910NZZ0900j(8)" "(8);:ZZ1900G$(G$,(G$)1):ZZZZ1:910G$"":ZH0:ZG0:G1$""G1$:G1$(8)1010:ZH(G1$):ZH81030W91ZG0ZH27G$(13): ZH13G$"+0"9105G1$"0"ĭ(G$,1)"-"(G$,1)"+"910[ZH120ZH121ZHZH32:G1$(ZH)z(ZH88ZH89)AV$"N"910ZH47ZH58ĭ(G$,1)"X"(G$,1)"Y"910ZH43ZH45ZH88ZH89928ZH47ZH57910ZZ0930:G1$"X"G1$"Y"āX