I need to figure out how to solve the equation x-squared y-squared+xy=1 i have no clue. I would appreciate any help!

Question

did you mean (x^2)(y^2) + xy = 1 ???

If so, are you solving for x or y?

Suggestion: let xy = a, then you have the equation a^2 + a - 1 = 0

solve it as a quadratic and a = (-1 +-sqr(5))/2

so xy = (-1+-sqr(5))/2 or the other root.
solve this for either x or y.