I have never solved any system consisting of squared numbers. I have been trying to figure this one out now for a while without any luck.

x^2 - y^2 = -(15/4)

2xy = 2

Basically, what I would like to do is

2xy = 2 <=> xy = 1 <=> x = 1 / y

then insert that into the top equation, but doing so will give me a new grade four equation, which cannot be right?