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Chapter 4: Q. 22 (page 385)

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

4x=3y+78x-6y=14

Short Answer

Expert verified

The solution of the system 4x=3y+78x-6y=14 has infinity many solutions.It is found by graph as,

Step by step solution

01

Step 1. Given information.

Consider the given system of linear equations,

4x=3y+78x-6y=14

02

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

Find slope and y-intercept of the first equation.

4x=3y+74x-7=3y(43)x-73=y

Here the slope is m=43and, the y-intercept b=-73.

03

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

Find slope and y-intercept of the second equation.

8x-6y=14-6y=-8x+14y=43x-73

Here the slope is m=43and, the y-intercept isb=-73.

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 equation true.
  • Therefore,there are infinity many solotions to this system.

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