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.

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

 

x + x*y + 1 = y + x*y

y = x + 1

x*y = x(x+1) (parabola) 

Posted by Benny on 2012-01-28 15:35:50