# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #4x+5y=-2# and #4y-x=11#?

##### 2 Answers

Jun 11, 2018

Consistent system.

Solution:

#### Explanation:

When you graph the functions, you come up with two lines that lie as follows in the Cartesian plane:

You will notice there is a single intersection (namely **intersection** is the **solution** of the system of equations. Since there is at least one solution to this system of equations, it is called **consistent**.

In some cases you will plot a system and there will be no intersection. This would be an example of an inconsistent system.

Jun 11, 2018

#### Explanation:

Writing your System in the form

multiplying the second equation by

so

we get

so