Chapter 6, Problem 16CT

To determine

To determine a system of two linear equations that has no solution.

Answer to Problem 16CT

  $y=5x-2$

  $y=5x-5$

Explanation of Solution

Given:

System of two linear equations

 A system of linear equations has no solution when the graphs are parallel.

A system of linear equations has no solution when there is no intersection or common point between the graphs of the two linear systems.

Let’s discuss an example,

Taking two linear systems,

  $\Rightarrow y=5x-2$

  $\Rightarrow y=5x-5$

As the equations have slope value same, that is $5$.

This means that the lines must be parallel. And since the  y -intercepts are different, we know the lines are not on top of each other.

Graph:

  

Conclusion:

Therefore, $y=5x-2$ and $y=5x-5$ are the system of two linear equations that has no solution.