SOLUTION: 3x-y=-6 2x+3y=7

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Question 1092356: 3x-y=-6
2x+3y=7

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

When both equations are given to you in the form Ax+By=C, by far the easiest way to solve the system of equations is by eliminating one of the variables.

You are given
3x-y+=+-6
2x%2B3y+=+7

Since the y terms have coefficients that are opposite signs, my preference is to multiply one or both equations by appropriate constants so that the coefficients of y in the two equations are opposites; then adding the two equations will eliminate y, leaving an equation in just x that I can solve. Then I use that value of x in one of the original equations to solve for y.

9x-3y+=+-18 [multiply the first equation by 3]
2x%2B3y+=+7
11x+=+-11 [add the two equations]
x+=+-1
2%28-1%29%2B3y+=+7 [set x to -1 in the second equation]
-2%2B3y+=+7
3y+=+9
y+=+3

The solution is (x,y) = (-1,3).