# 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?

Jul 20, 2018

the system is consistent

#### Explanation:

$9 x - 4 y = 12$ .........(1)
$4 y - 9 x = - 12$ ...(2)

Rearrange the equations to get $y$ on the LHS, then graph

(1):

$9 x - 4 y = 12$ ........(1)

$- 4 y = - 9 x + 12$

$y = \frac{- 9 x + 12}{-} 4$
graph{(-9x+12)/-4 [-10, 10, -5, 5]}

(2):

$4 y - 9 x = - 12$ ....(2)

$4 y = 9 x - 12$

$y = \frac{9 x - 12}{4}$
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:

$9 x - 4 y = 12$ .........(1)

multiply both sides of eqn(1) by -1

$- 9 x + 4 y = - 12$

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