Question

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`?

Answer 1

Consistent system.

Solution: `(-3,2)`

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 `(-3,2)`) between the two lines. This is the geometric interpretation of a solution to the system. The 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.

Answer 2

`x=-3,y=2`

Explanation:

Writing your System in the form

`4x+5y=-2`
`-x+4y=11`
multiplying the second equation by `4` and adding to the first we get

`21y=42`
so

`y=2`
we get

`-x+8=11`

so

`x=-3`