Question

The system 2x − 4y = 6 and x − y = −3 is independent. Replacing x − y = −3 with which of the following equations would result in an inconsistent system?

Answer 1

x-2y= -3
You could solve each of the the systems and use which one has no solutions, and that will be the inconsistent system.

Answer 2

The answer is x-2y=0

Explanation:

A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel.

Replacing x − y = −3 with x-2y=0 makes the system inconsistent because both x-2y=0 and 2x-4y=6 lines will be parallel.