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Chapter 4: Q 7 (page 385)

In the following exercises, solve the following systems of equations by graphing.

y=x+2y=-2x+2

Short Answer

Expert verified

The solution to the linear equations is (0,2).

Step by step solution

01

Step 1. Given information 

The given linear equations are

y=x+2y=-2x+2

02

Step 2. Solving equations for the intersection points 

First, solve both of these equations for y such that their slopes and y intercepts may be easily graphed.

And find the slope and y-intercept by solving the first equation for y.

y=x+2Heretheslopeism=1Andthey-interceptisb=2AgainSolvethesecondequationfory,andfindtheslopeandy-intercept.y=-2x+2Heretheslopeism=-2Andthey-interceptisb=2

03

Step 3. Graph obtained 

04

Step 4. Checking the equation

Check:Firstsubstitutex=0,y=2Intotheequationy=x+2.y=x+22=0+22=2Thisistrue.Alsosubstitutex=0,y=2intotheequationy=-2x+2y=-2x+22=-2(0)+22=0+22=2Thisistrue.Thesolutionofthesystemoflinearequationsis(0,2)

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