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Chapter 4: Q 11 (page 385)

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

x+y=-4-x+2y=-2

Short Answer

Expert verified

The solution of the system of linear equations is (-2,-2).

Step by step solution

01

Step 1. 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.

x+y=-4y=-x-4Heretheslopeism=-1Andthey-interceptisb=-4

Again find the slope and y-intercept by solving the Second equation for y.

-x+2y=-22y=x-2y=12脳x-22y=12脳x-1Heretheslopeism=12Andthey-interceptisb=-1

02

Step 2. Graph obtained

03

Step 3. Checking the equations

Check:Firstsubstitutex=-2,y=-2intotheequationx+y=-4-2-2=-4-4=4Thisistrue.

Alsosubstitutex=-2,y=-2intotheequation-x+2y=-2-x+2y=-2-(-2)+2(-2)=-22-4=-2-2=-2Thisistrue.

Alsosubstitutex=-2,y=-2intotheequation-x+2y=-2-x+2y=-2-(-2)+2(-2)=-22-4=-2-2=-2Thisistrue.

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