00020002010012LinearEquation.ACT0003020013GraphAndAnalyse.EAC01000000b887Dkx[Graphing And Analyzing[Linear Equation\Author\PMun Chou, Fong Mathsroof Consultancy Malaysia. e-mail: mcfong@mathsroof.com[[ OBJECTIVE[To solve equations of[the form A+B=0 and[A+B=C by using a graph[analysis approach.[[We begin by helping you[to get familiar with the[graphing of A+B=y using[drag and drop. [ [ Exercise 1:[Lets begin the exercise [by letting A+B=y. The[graphing is performed by[modifying A and B.[Here, initial values of 1[are assigned to both A [and B.R clear_a_zRdoneR1AR1R1BR1R[Step 1[To graph the line,tap on[GraphStrip,select y=A+B[and drag it into the graph [window.[ \ GraphStripGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`` `(10qy`#YuY u`u``Rcx O[Step 2[Now scroll up and assign[-2 to B.Remember to tap[[EXE] after the change.[[Step 3 [Immediately after, tap[on the graph window.[To which direction did the[ line shift?[Repeat Step 2 to Step 3[with these value pairs.[i)A=2, B=1; ii)A=-2, B=3[[[We are now ready to [work on Example 1.[[ Example 1:[Our task is to solve the[equation of 2+7=0.[We are going to use a[graph analysis approach[in solving it. [To avoid confusion,C and[D are used in place of A[and B.[[ Solution:[Step (i)[Let 2+7= and assign[2 and 7 to C and D, as[similar to Exercise 1.[R2CR2R7DR7R[ Step (ii)[Tap on GraphStrip 2.[Select y=C+D and drag[it into the graph window[\ GraphStrip 2Graph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P``)) `(10qy`#YuY qBqAYx`6!&2 O[The graph is now drawn.[To analyse the graph:[ Step (iii)[While in graph window,tap[on [Analysis] [G-Solve][ [x-cal]. Enter 0 for[y-value and tap [OK].[This graph analysis shows[that x=-3.5 when y is 0.[[Integrating what we have[observed so far:[In Step (i), we let C=2[and D=7, hence we can[write y=C+D as y=2+7[We also learned from the[graph analysis that when[ y=0, x=-3.5.[ This implies that the[solution to 2+7=0 is[ x=-3.5. ~[[ Exercise 2:[Use the graph analysis[approach to find the[ solution to:[i) 7+16=0; ii) -18+19=0[[[Let's extend the graph[analysis approach to [equation of the form[a+b=c where c0.[[Exploration 1:[Suppose we are given the[ equation of 74 +5=3.8.[Try the tasks below.[[(1) Perform appropriate[algebraic steps to reduce[ the equation 74+5=3.8[to the form of M+N=0.\Use Here4R clear_a_zRdoneRGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss aseq_histbNewFolde system]listsystem^]=systemssystem]listsystem^]=systemssystem]listsystem^]=systemssystem]listsystem^]=systemssystem]listsystem^]=systemssystem]listsystem^]=systemssystem]listsystem^]=systemssystem]listsystem^]=systemssystem]listsystem^]=systemssystem]listsystem^]=systems  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[[(2) Rewrite the equation[you have found in (1) as[ y=M+N. [[Key,your answer to (2),[into y1 in Graphing strip.[Then tap to graph y1.\GraphingGraph2D@ Graph3DT LISTSYS`4NModify $ STATCALC NSTATSYS \NSequence, SheetH| Sheet3D| SolveEq@SolveLwrD SolveUprP StupFLG1\(StupListD StupPict$ ViewWind y1H$ 0 < H T ` l x           ! " # $ % &, '8 (D )P *\ +h ,t - . 0 1 2 3 4 5 E F H I J K L( M4 N@ OL PX Qd Rp S| T ] ^ _ ` a b      system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $   3x7*x/4+6/5`P`P`p`p `(10qy`#YuY qBqFY` P[[While in Graph window,[[(3) Tap [Analysis] [[G-Solve] to analyse the[graph to find value of x[when y is equal to 0.[ \Exploration Notes(1),(2) Performing the subtract operation of a+b-c=c-c gives us the equation of 1.75+1.2=0. Rewriting it we have y=1.75+1.2 (3) When y=0, x value is approximately 0.6857.[[Complete the workings in[Algebra strip to solve[74+5=3.8 algebraically.\AlgebraR clear_a_zRdoneR74+5=3.8 eq1R7x4+5=195RGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[[What is the solution from[ your working?[Compare the solution with[answer from the graph[analysis in (3). Are they[ the same?[[Describe what your may [have observed from this[ activity.[[###Exploration Notes##[- In (1),(2) and (3) we[ transformed 74+5=3.8[into another form before[solving it using the graph[analysis. In fact result[of the analysis is the[ solution to 74 +5=3.8.\ Tap to see. Rsolve(74 +5=3.8)Rx=-2435Rsolve(74 +5=3.8)Rx=- 0.6857142857RGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[[- The solution from the[algebraic method verifies[the solution obtained[using graph analysis.[#######################[[Hence we've discovered[the key in solving linear[equations of any form[using the graph analysis[approach is to reduce[them into the form of[Mx+N before graphing.[[ Exercise 2:[Use the graph analysis[approach to solve these[linear equations.[i) 12+8=3.[ii) 12 +8=-2+45.[Hints: [As seen in Exploration 1,[reduce both equations in[to the form of A+B=0[first.[\Use here 4R clear_a_zRdoneRGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[ \ Analyse here Graph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[eAct A \B \C \D \Eq1PPF 3.8 xweq1PPF 3.8 gPR x ݂>_weq2llF 8     = =dxeq3DDF d38 =  x eq5S)/(eqb1PPF 3.8 ;\x;020015SolvingLinearEqua.EAC01000000b851Dkx[Solving Linear Equation\Author\PMun Chou, Fong Mathsroof Consultancy Malaysia. e-mail: mcfong@mathsroof.com[[ OBJECTIVE[I.To study the underlying[algebraic concepts and[strategy in the process[of solving linear equation[problem.[[When solving any linear[equations, we normally[perform the following 4[steps:[STEP 1[Arrange all terms on left[side of equation.[STEP 2[Simplify the equation to[the form a+b=0.[STEP 3[Solution is thus =-ba.[STEP 4[Verify the solution.[[[ Example 1[Solve 7+5=3 for .[[ Solution:[Tap on solution strip to[see sequence of solution[perfoming steps 1,2 and[3 with algebraic approach[\Solution strip R clear_a_zRdoneR7+5=3eq1R7x+5=3xR eq1-3eq2R4x+5=0R eq2-5eq3R4x=-5Req314Rx=-54RGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[Perform the verification[step 4 with NumSolve.[- tap once on Numsolve[ strip below[- select 7+5=3 and [ drag it into }[- tap [Solve] icon at[ toolbar twice[\NumSolve stripGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D |i |Dkx $ `P`P`p`p `(10qy`#YuY ` O[The value for x displayed[should correspond to the[solution, which is -1.25.[[[Exploration 1:[Replace 3 at the step['eq1+3eq2' in the [Explore Strip below with:[(i)4, (ii)(-3)[Tap [EXE] after each [ replacement.[\Explore Strip R clear_a_zRdoneR95-8=-3eq1R9x5-8=-3xR eq1+3eq2R24x5-8=0R eq2+8eq3R24x5=8Req3524Rx=53RGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[Describe what happens[after each replacement.[[Exploration 2:[Return to Explore Strip[ above and replace 95[in '95-8=-3eq1' with[-3 and tap [EXE].[Describe what happened[and why.\Exploration Notes- Try to understand the algebra in each chosen solution step in attaining the solutions for both explorations. - An error message is displayed in Exploration 2 after the replacement. This is because equation -3-8=-3 is inconsistent.[[[ Exercise 1:[Complete the solution for[each problem. \ Problem (i)0R clear_a_zRdoneR12-5=12 +8eq1R12x-5=x2+8R eq1-8eq2R12x-13=x2RGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[\ Problems (ii)R clear_a_zRdoneR137- =7.8+6eq1R-x-73=6x+395RGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[[ Exercise 2:[Use concept and strategy[employed in Example 1 to[simplify,solve and verify:[(i) 15-8=12(+2.5)[(ii) 15+5=2-15[(iii) 2-95 =17.8+2\Use here ------ 4R clear_a_zRdoneRGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O\Use here ------ Graph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! " # $ % & ' ( ) *, +8 ,D -P .\ 0h 1t 2 3 4 5 E F H I J K L M N O P( Q4 R@ SL TX ]d ^h _l `p at bx |     system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i Dkx $ `P`P`p`p `(10qy`#YuY ` O[[Exploration 3:[Lets explore further by[representing the equation[7+5=3 from Example[1, graphically.[- Tap once on Geometry[ strip below.[- Select 7+5=3 and[ drag-drop it into the[ window.[\Geometry Strip ``vrALCuxy[Do you see a vertical [line appearing to the left[ of y-axis? [- Tap to select this line[- Tap on button at the[ right of toolbar.[What do you see in the[measurement box?[[###Explore 3 Notes###[- the line appeared in[the Geometry Strip is in[fact the solution to [7+5=3, i.e. =-1.25.[[- So we have a choice[to verify the solution by[using Geometry Strip.[#######################[[ Exercise 3[ The equation,[    -32+5=-16[can be express in the[ form A+B=0.\Use here R clear_a_zRdoneR-32+5=-16eq1Ry-32+y5=y-16RrGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! 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