SOLUTION: Solve the following system of equations using the addition (elimination) method. Be sure to state the solution to the system. x+2y=-7 2x+3y=-12

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Question 79778: Solve the following system of equations using the addition (elimination) method. Be sure to state the solution to the system.
x+2y=-7
2x+3y=-12
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:
1%2Ax+%2B+2%2Ay+=+-7
2%2Ax+%2B+3%2Ay+=+-12
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 2 as our coefficient for x, to get -1 we have to multiply all terms of the second equation by -1%2F2 which is equal to -0.5.

Multiplying, we get on our second equation:%282%2A-0.5%29x+%2B+%283%2A-0.5%29y+=+-12%2A-0.5
-1%2Ax+%2B+-1.5%2Ay+=+6

Adding both equations we get:

%281%2B-1%29x+%2B+%282%2B-1.5%29y+=+%28-7%2B6%29

Since 1 and -1 cancel out, we have a linear equation:Therefore, we know that y = -2.

Plugging that in into the first equation gives us:

1%2Ax+%2B+2%2Ay+=+-7
1%2Ax+%2B+2%2A-2+=+-7
1%2Ax+%2B+-4+=+-7
1%2Ax+=+-7+-+-4
x+=+%28-7+-+-4%29%2F1
x+=+-3%2F1
x+=+-3

Therefore, our answer is:

system%28+x=-3%2C+y=-2+%29


So the solution is (-3,-2)