Lesson 3.2

Lesson 3.2Explore 1: Solving Equations using a Graphical Method1. Solve this equation algebraically.2x +3 = -3x -7,,# rJLet's use what we learned about systems of equations in the last lesson and try anothermethod for solving an equation.. Using the E Editor on your graphing calculator, enter 2x + 3 into Yr.. Using the E Editor on your graphing calculator, enter -3x - 7 into Yz.. When you enter -3x - 7 into Y2, select either the thick line style or the path line style to theleft of Yz, so that you can tell the two equations apart.. Using the standard window, graph the two functions."Use the l2ndllTFE0E-l or lcnlc] feature to find the solution, or point of intersection, of thissystem of.equations.Ptotl Pl+tl P1+t3r E?H+3E "3H-7\Y3='-Vq=-'V5=rVE='"VF=IHHmin= -18Hmax= t ffHscl=1Vnin= -18Vnqa:q= 1BVscl=1Hr'es=l2. What is the point of intersection, or solution, to the system?3. Do you think that the solution to the system of equations is related to the algebraic solutionyou found in question 1? WhY?4. Show how you could check your solution for the equation on the Home Screen of yourgraphing calculator.O 2008 Region 4 Education Service CenterAll rights reserved.Accelerated Curriculum for Mathematics: Grade 10 TAKSTMVolume 1: Algebra Connections139

j Lesson 3.2+frthe next four problems, solve the equation algebraically. Then solve graphically by placingtne left side of the equation in Yr and the right side in yz. \Mat do you notice?5. 3+6x =2x-5 6. 3{x -4} = 2x -9Algebraic solutionAlgebraic solutionGraphtcal solutionGraphical solution7. 5(x+2)=x-4 8. 2x =1.S(4x+3)-2Algebraic solutionAlgebraic solutionurapntcat soluttonGraphical solutionAccelerated Curriculurn for Mathematics Grade 10 TAKSr',,Volume '1 Algebra Connections140O 2008 Region 4 Education Service CenterAll rights reserved.

Lesson 3.2 -#Explore 2: Simplifying Expressions, How toCheck Your Answerssolve this equation using both the algebraic method and thegraphical method.5(x+2)=5x+10Plotl PlotZ P1ot3rVi =rVt=r.V3=rVlr='r!5='.VE=rt,J 7 = '32 Re:c-J :able values from your graphical solution. Wlrat do you notice?3 How many solutions does this equation have? Why?4 Simplify the exPression: 3x + 2x5 Enter 3x + 2x in Yr in the Y= editor. Enter your answer fromquestion4 in Y2 in theY= editor. Use the path line style for Yz. Sketch your graph Fill in the table. What do Younotice?Fl*tl Fl+tt F1+t3rr/t =4tt't=. I t--.'.Vq=r.Vsrr?i=t.V7=-i'1r)L tO 2008 Region 4 Education Service CenterAll rights reserved.Accelerated Curriculum for Mathematics: Grade 10 TAKSTMVolume 1: Algebra Connections141

iilLesson 3.2IaaaSimplrfy each expression in the table below.Enter the original expression in Y1.Enter the simplified expression in y2.Be sure to use either the thick line or the path line for yr.Draw a sketch of your graph.6. a-{x-2) 7. 2fu,+,71+,2{x-3)Simplifu algebraically.SimplifiT algebraically.'necK your answer graphically.Jraw a sketch.Check your answer graphically.Draw a sketch.lrVr = |l+Vz=Il''Vi= |ItVr=iI'Vs=jl"Vt=|Il''V r =Accelerated Curricuiurn for Mathematics Grade 10 TAKSnJVolume 1 Algebra Connections142O 2008 Region 4 Education Service CenterAll rights reserved

Lesson 3.2$ '8. 5-2tx+5)+3xSimplify algebraicallY.9. *3tx-4)-(x+2)-5Simplify algebraicallYCheck your answer graPhicallY.Draw a sketehP'lrtl'..t'rt 1 ={j\rJ i ='rtf i =t'.t't \=, l I--.. T :.-'..V 6 ='..Lf, p =P'lotl P'lotlCheck your answer graPhicallY.Draw a sketch.P'lotl Pl'.rti P'l+t3\Vi =Vt='rV3="'liJ q =. I t--r.Y:.-. I I\.Y h- --'t!tl =O 2008 Region 4 Education Service CenterAll rights reserved.nccefer"teO Curriculum for Mathematrcs: Grade 10 TAKSTMVolume 1. Algebra Connections143