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
PJ
Jul 20, 2018

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

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