Question

A system of equations is graphed on the coordinate plane.

y=-2x-3
y=-2x+2 how would you classify this system of equations?

Answer 1

Inconsistent

Explanation:

we know that

If a system of two linear equations have at least one solution, it is said to be consistent .

If a consistent system has exactly one solution, it is independent .

If a consistent system has an infinite number of solutions, it is dependent .

If a system of two linear equations no have solution, it is said to be inconsistent.

Remember that

When solving a system of linear equations by graphing, the solution of the system is the intersection point both graphs

In this problem we have

`y=-2x-3` ----> equation A

`y=-2x+2` ----> equation B

Their slopes are equal (m=-2) and their y-intercept are different

so

we have two different parallel lines

The lines not intersect

therefore

The system has no solution, because is inconsistent