Chapter 6.1, Problem 51HP

To determine

To find: Three equations such that they form three system of equations with $y=5x-3$ .

Answer to Problem 51HP

  $y=5x+3$ ; $y=-5x-3$ ; $2y=10x-6$

Explanation of Solution

Given information:

  $y=5x-3$

Sample answers are

  $y=5x+3$ ; $y=-5x-3$ ; $2y=10x-6$

The first equation is parallel to the original equation,So there is no intersection, which makes the system in consistent.

  

Here red line represents $y=5x+3$ and blue line represents $y=5x-3$

The second equation has one intersection , which makes the system consistent and independent.

  

Here red line represents $y=-5x-3$ and blue line represents $y=5x-3$

The last equation is the same as the Original equation, which makes the system consistent and dependent.