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Chapter 4: Q 15 (page 385)

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

x+3y=-6y=-43x+4

Short Answer

Expert verified

The solution of the system of the linear equation is (6,-4).

Step by step solution

01

Step 1. Given information.

Given the system of linear equations,

x+3y=-6y=-43x+4

02

Step 2. Solve the first equation for y, and find the slope and y-intercept.

Write the equation in slope-intercept form.

x+3y=-63y=-x-6y=-13x-63y=-13-2

Here the slope is localid="1658763876892" m=-13and the y-intercept is b=-2.

03

Step 3. Solve the second equation for y and the slope and intercept of y.

The equation is given in the standard form. So,

y=-43x+4

The slope is m=-43and the y-intercept b=4.

04

Step 4. Graphs for both the lines.

The obtained graph form the given equation is,

05

Step 5. Check the solution.

First substitute x=6,y=-4into the equationx+3y=-6.

localid="1644923746470" x+3y=-66+3(-4)=-66-12=-6-6=-6

This is true.

Also substitute x=6, y=-4 into the equation y=-43x+4.

localid="1644923760696" -4=-43(6)+4-4=-8+4-4=-4

This is true.

Therefore the solution of the system of the linear equation is (6,-4).

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