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Chapter 4: Q. 21 (page 385)

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

x=-3y+42x+6y=8

Short Answer

Expert verified

The solution of the system x=-3y+42x+6y=8has infinity many solutions.It is found by a graph as,

Step by step solution

01

Step 1. Given information.

Consider the given system of linear equations,

x=-3y+42x+6y=8

02

Step 2. Solve the first equation for y.

Find slope andy-intercept of the first equation.

x=-3y+4-3y=-x+4y=(13)x-43

Here the slope is m=13and the y-intercept isb=-43.

03

Step 3. Solve the second equation for y, and find slope and y-intercept.

Find slope and y-intercept of the second equation.

2x+6y=86y=-2y+8y=(-13)x+43

Here the slope is m=-13and, the y-intercept b=43.

04

Step 4. Graph both the lines.

The graph of both equations on the same plane is drawn below,

  • The lines are the same.
  • Since every point on the line makes both equations true, there are infinity-ordered pairs that make both equations true.
  • Therefore, there are infinity many solutions to this system.

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