Question

Is the system of equations is consistent, consistent and coincident, or inconsistent?

y=−x−13y=−3x+2



Select the correct answer from the drop-down menu.



Graph of two lines on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1.

Answer 1

Is a consistent independent system

Explanation:

we know that

If a system has 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 not have solution, it is said to be inconsistent

In this problem we have

`y=-x-13` ----> equation A

`y=-3x+2` ----> equation B

Solve the system by graphing

The solution is the intersection point both graphs

The solution is the point (7.5,-20.5)

see the attached figure

therefore

Is a consistent independent system