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Chapter 4: Q. 20 (page 385)

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

x+3y=4-2x-6y=3

Short Answer

Expert verified

The system of equations x+3y=4-2x-6y=3has no solution and it can be seen in the graph as,

Step by step solution

01

Step 1. Given information.

Consider the given System of linear equations,

x+3y=4-2x-6y=3

02

Step 2. Solve the first equation for y.

Find the slope and y-intercept of the first equation.

x+3y=43y=-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 the slope and y-intercept.

Find the slope and y-intercept of the second equation.

-2x-6y=3-6y=2x+3y=(-13)x-12

Here the slope is m=-13and, the y-intercept isb= -1/2.

04

Step 4. Graph both the lines.

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

Image Caption

  • The lines are parallel.
  • Since, no point in both lines, there is no ordered pair that makes both equations true.
  • Therefore, no solution to this system.

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