SOLUTION: Solve the simultaneous equation 4x+y=22 x+4y=16

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Question 81590This question is from textbook
: Solve the simultaneous equation
4x+y=22
x+4y=16
This question is from textbook

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:
4%2Ax+%2B+1%2Ay+=+22
1%2Ax+%2B+4%2Ay+=+16
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 -4 we have to multiply all terms of the second equation by -4%2F1 which is equal to -4.

Multiplying, we get on our second equation:%281%2A-4%29x+%2B+%284%2A-4%29y+=+16%2A-4
-4%2Ax+%2B+-16%2Ay+=+-64

Adding both equations we get:

%284%2B-4%29x+%2B+%281%2B-16%29y+=+%2822%2B-64%29

Since 4 and -4 cancel out, we have a linear equation:Therefore, we know that y = 2.8.

Plugging that in into the first equation gives us:

4%2Ax+%2B+1%2Ay+=+22
4%2Ax+%2B+1%2A2.8+=+22
4%2Ax+%2B+2.8+=+22
4%2Ax+=+22+-+2.8
x+=+%2822+-+2.8%29%2F4
x+=+19.2%2F4
x+=+4.8

Therefore, our answer is:

system%28+x=4.8%2C+y=2.8+%29