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.

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