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)
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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