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Chapter 4: Q 10 (page 385)

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

y=23x-2y=-13x-5

Short Answer

Expert verified

The solution of the system of linear equations is (-3,-4).

Step by step solution

01

Step 1. Given information  

Two linear equations are

y=23x-2y=-13x-5

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=23脳x-2Heretheslopeism=23Andthey-interceptisb=-2

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

y=-13脳x-5Heretheslopeism=-1/3Andthey-interceptisb=-5

03

Step 3. Graph obtained  

04

Step 4. Checking the equations 

Check:Firstsubstitutex=-3,y=-4intotheequationy=23x-2-4=23(-3)-2-4=-2-2-4=4Thisistrue.

Alsosubstitutex=-3,y=-4intotheequationy=-13脳x-5y=-13脳x-5-4=-13脳(-3)-5-4=1-5-4=4Thisistrue.

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