How do you solve this system of equations: −5x−7y=−15and5x+9y=5?

1 Answer
Max K.
Dec 7, 2017

x=10
y=−5

Explanation:

Add the two equations together first:

→ −5x−7y=−15
(+) 5x +9y=5

Adding both left sides of each equals sign together, the x values cancel out ( −5x+5x=0) , and −7y+9y=2y

Adding both right sides of the two equations −15+5=−10

That leaves us with 2y=−10
then divide both sides by 2 to get:
y=−5

You can then fill that into either of the original equations to find x

5x+9y=5
5x+9(−5)=5
5x−45=5
Add 45 to both sides
5x=50
divide both sides by 5
x=10

It's also recommended to check your answer in the other equation:

x=10
y=−5

−5x−7y=−15
−5(10)−7(−5)=−15
−50+35=−15
−15=−15

Correct! :)

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