Question

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`?

Answer 1

the system is consistent

Explanation:

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

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

(1):

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

`-4y=-9x+12`

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

(2):

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

`4y=9x-12`

`y=(9x-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:

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

multiply both sides of eqn(1) by -1

`-9x+4y=-12`

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