SOLUTION: Solve the system of equations using the addition method. x+y=5 3x-4y=-20

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Question 82435: Solve the system of equations using the addition method.
x+y=5
3x-4y=-20
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+1%2Ay+=+5
3%2Ax+%2B+-4%2Ay+=+-20
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 3 as our coefficient for x, to get -1 we have to multiply all terms of the second equation by -1%2F3 which is equal to -0.333333333333333.

Multiplying, we get on our second equation:%283%2A-0.333333333333333%29x+%2B+%28-4%2A-0.333333333333333%29y+=+-20%2A-0.333333333333333
-1%2Ax+%2B+1.33333333333333%2Ay+=+6.66666666666667

Adding both equations we get:

%281%2B-1%29x+%2B+%281%2B1.33333333333333%29y+=+%285%2B6.66666666666667%29

Since 1 and -1 cancel out, we have a linear equation:Therefore, we know that y = 5.00000000000002.

Plugging that in into the first equation gives us:

1%2Ax+%2B+1%2Ay+=+5
1%2Ax+%2B+1%2A5.00000000000002+=+5
1%2Ax+%2B+5+=+5
1%2Ax+=+5+-+5
x+=+%285+-+5%29%2F1
x+=+0%2F1
x+=+0

Therefore, our answer is:

system%28+x=0%2C+y=5.00000000000002+%29