My technique for this problem, wasn't the best, but it lead me to the correct answer:
x^2y^2-xy = 6
you can factor out xy, therefore:
xy(xy-1) = 6
xy has to be an integer, so the product of a certain integer and that integer minus 1 = 6, so I figured the intgers could be 3 and 2
so
X = 3; y=1
or
x=1; y=3
from here I just plugged in X into the options:
I. 1/(2x) = 1/6 or 1/3; no good- eliminate A, C, & D
** only B & E remain, II must work
III. 3/x = 1 or 3, this works- choose E
If my post causes more harm than, good I apologize. Once I realized that I couldn't simply isolate y, I realized this problem had a solution that wasn't intuitive to me, so I tried the best I could and it worked (in under two minutes). I think that's the moral of my story.
Naturally Cramya has an great solution- use hers for this type of problem
Thanks Cramya!
- Jay
