How do you solve the system x + y = 14x+y=14 and -x + y = 16−x+y=16?

1 Answer
Alan P.
Jul 19, 2016

color(green)((x,y)=(-1,15))(x,y)=(−1,15)

Explanation:

Given
[1]color(white)("XXX")x+y=14XXXx+y=14
[2]color(white)("XXX")-x+y=16XXX−x+y=16

Adding [1] and [2] gives
[3]color(white)("XXX")2y=30color(white)("XX")rarrcolor(white)("XX")y=15XXX2y=30XX→XXy=15

Subtracting [2] from [1] gives
[4]color(white)("XXX")2x=-2color(white)("XX")rarrcolor(white)("XX")x=-1XXX2x=−2XX→XXx=−1

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