SOLUTION: 1/x + 1/y = 1/2 solve for x and y

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Question 35691: 1/x + 1/y = 1/2
solve for x and y

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
To solve for either x or y, the first step is to clear the fractions by multiplying both sides by the LCD which is 2xy

1%2Fx+%2B+1%2Fy+=+1%2F2
2xy%2A%281%2Fx%29+%2B+2xy%2A%281%2Fy%29++=+2xy%2A%281%2F2%29
2y+%2B+2x+=+xy+

Now, to solve for x, get all the x terms on one side by subtracting 2x from each side:
2y+=+xy+-+2x

Factor the x, so as to get the x's all in one place:
2y+=+x%28y-2%29+

Divide both sides by (y-2):
%282y%29%2F%28y-2%29+=+%28x%2A%28y-2%29%29%2F%28y-2%29
%282y%29%2F%28y-2%29+=+x

NOW, to solve for y in terms of x, go back to the equation 2y+%2B+2x+=+xy+.
To solve for y, get all the y terms on one side by subtracting 2y from each side:
2x+=+xy+-+2y

Factor the y, so as to get the y's all in one place:
2x+=+y%28x-2%29+

Divide both sides by (x-2):
%282x%29%2F%28x-2%29+=+%28y%2A%28x-2%29%29%2F%28x-2%29
%282x%29%2F%28x-2%29+=+y

R^2 at SCC