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is 5,-4 a solution of the system 2x+6y=-12 2x+y=6

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To answer this question, you need to see if the ordered pair solves both equations.  If it is a solution to both, and only to both, then it solves the system.  If it doesn't work in either one, it is not a solution.  So, find out if:

2(5) + 6(-4) = -12 and if 2(5) = (-4) = 6.

If both are yes, then it is the solution.  Otherwise, it isn't.