SOLUTION: I don't know if this one falls into this category or not, but could someone help me please? Solve the system by addition 5x+9y=-12 x-2y=-10

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Question 82222: I don't know if this one falls into this category or not, but could someone help me please?
Solve the system by addition
5x+9y=-12
x-2y=-10

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Linear Systems by Addition
We'll solve the system:
5%2Ax+%2B+9%2Ay+=+-12
1%2Ax+%2B+-2%2Ay+=+-10
by elimination by addition.To eliminate by addition, we need to set both coefficients of x to numbers with changed signs, i.e a and -a. Since in the second equation we have 1 as our coefficient for x, to get -5 we have to multiply all terms of the second equation by -5%2F1 which is equal to -5.

Multiplying, we get on our second equation:%281%2A-5%29x+%2B+%28-2%2A-5%29y+=+-10%2A-5
-5%2Ax+%2B+10%2Ay+=+50

Adding both equations we get:

%285%2B-5%29x+%2B+%289%2B10%29y+=+%28-12%2B50%29

Since 5 and -5 cancel out, we have a linear equation:Therefore, we know that y = 2.

Plugging that in into the first equation gives us:

5%2Ax+%2B+9%2Ay+=+-12
5%2Ax+%2B+9%2A2+=+-12
5%2Ax+%2B+18+=+-12
5%2Ax+=+-12+-+18
x+=+%28-12+-+18%29%2F5
x+=+-30%2F5
x+=+-6

Therefore, our answer is:

system%28+x=-6%2C+y=2+%29