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Chapter 4: Q. 23 (page 385)

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

2x+y=6-8x-4y=-24

Short Answer

Expert verified

The solution of the system 2x+y=6-8x-4y=-24 has infinitely many solutions. It is found by the graph as,

Step by step solution

01

Step 1. Given information.

Consider the given system of linear equations.

2x+y=6-8x-4y=-24

02

Step 2. Solve the first equation for y.

Find slope andy-intercept of the first equation.

2x+y=6y=-2x+6

Here the slope m=-2 and the y-intercept is b=6.

03

Step 3. Solve the second equation for y.

Find slope and y-intercept of the second equation.

-8x-4y=-24-4y=8x-24y=(-2)x+6

Here the slope is m=-2and, the y-intercept b= 6.

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 infinitely many solutions to this system.

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