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Simultaneous Settlement (Posted on 2012-01-27) Difficulty: 3 of 5
Without solving for x and y, determine all possible values of x*y in this simultaneous equation:

x+x*y = 8 and, y+x*y = 9

Note: Solving for 1/x, 1/y, -x or -y is similarly NOT allowed.

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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One way Comment 8 of 8 |

Not sure what the previous answers were, but here is one way:

x=8-xy ; y=9-xy
multiply these together
xy=(8-xy)(9-xy)
xy=72 - 17xy + (xy)^2
(xy)^2 -18xy + 72 = 0
xy = (18 +/- sqrt(324-288))/2
xy = 9 +/- 3
xy = {6, 12}


  Posted by Larry on 2012-01-28 15:45:54
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