SOLUTION: Solve the system by addition: -5x+2y=10 x-3y=11

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Question 82569: Solve the system by addition:
-5x+2y=10
x-3y=11

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+2%2Ay+=+10
1%2Ax+%2B+-3%2Ay+=+11
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%2A5%29x+%2B+%28-3%2A5%29y+=+11%2A5
5%2Ax+%2B+-15%2Ay+=+55

Adding both equations we get:

%28-5%2B5%29x+%2B+%282%2B-15%29y+=+%2810%2B55%29

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

Plugging that in into the first equation gives us:

-5%2Ax+%2B+2%2Ay+=+10
-5%2Ax+%2B+2%2A-5+=+10
-5%2Ax+%2B+-10+=+10
-5%2Ax+=+10+-+-10
x+=+%2810+-+-10%29%2F-5
x+=+20%2F-5
x+=+-4

Therefore, our answer is:

system%28+x=-4%2C+y=-5+%29