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Chapter 5: Q. 17 (page 595)

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

-x+y=-34x+4y=4

Short Answer

Expert verified

The solutions to the system of equations are:

x=2,y=-1

Step by step solution

01

Step 1. Given information.

We have:

-x+y=-34x+4y=4

02

Step 2. Find the intercepts.

We will find the x-intercept and y-intercept of both equations and use them to graph the lines.

The system of equations are:

-x+y=-34x+4y=4

x-intercept: substitute y=0:

localid="1647600186256" -x+0=-3x=3

X-intercept:3,0

role="math" localid="1647600263553" 4x+4(0)=44x=4x=1

X-intercept:1,0

y-intercept: substitute x=0:

-0+y=-3x=-3

Y-intercept: 0,-3

4(0)+4y=44y=4y=1

Y-intercept:0,1

03

Step 3. Use the intercept to draw the graph.

Graph the line and find the intersection point:

The lines intersect at 2,-1.

Therefore, the solutions are:

x=2,y=-1

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