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.

Nothing like as nice as Jer's, though:

By inspection, y=(x+1), then

x(x+2)=8 
y^2=9 
xy=(8/(x+2))*(9/(y)) 
(x+2)y^2x = 72 
x=(8-xy) 
y=(9-xy) 
(xy-10)(xy-9)(xy-9)(x y-8) = 72 
say, (z-10) (z-9)(z-9) (z-8) = 72 
z={6,12}

Posted by broll on 2012-01-27 14:27:38