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Chapter 5: Q. 20 (page 595)

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

-3x+y=-24x-2y=6

Short Answer

Expert verified

The solutions to the system of equations arex=-1andy=-5.

Step by step solution

01

Step 1. Given information.

We have:

-3x+y=-24x-2y=6

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:

-3x+y=-24x-2y=6

x-intercept: substitute y=0:

-3x+0=-2x=23x=0.667

X-intercept: 0.667,0

4x-2(0)=64x=6x=1.5

X-intercept: 1.5,0

y-intercept: substitute x=0

-3(0)+y=-2y=-2

Y-intercept:0,-2

4(0)-2y=6y=-3

Y-intercept:0,-3

03

Step 3. Use the intercept to draw the graph.  

Graph the line and find the intersection point:

The lines intersect at -1,-5.

Therefore, the solutions are:

x=-1,y=-5

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