# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #9x-4y=12# and #4y-9x=-12#?

##### 1 Answer

Jul 20, 2018

the system is consistent

#### Explanation:

Rearrange the equations to get

(1):

graph{(-9x+12)/-4 [-10, 10, -5, 5]}

(2):

graph{(9x-12)/4 [-10, 10, -5, 5]}

These 2 graphs are the same!

Check any point on line (1), it also exists on line (2).

So the system is consistent because there is a solution which satisfies both equations.

(actually there are an infinite number because both eqns plot the same line)

...........

Extra information:

We could also show this with algebra:

multiply both sides of eqn(1) by -1

this is the same as eqn (2), so the 2 eqns are consistent