x^2+y^2=2, xy=1, how to find x and y I have problems when doing these equations when I don't know any variable's value.
Can someone please explain how to do this and possibly give some tips when it comes to solving these problems?
Well, I know x = 1 and y = 1, but what about this one:
a-b=3, a:b=3:2, find a^2-b^2
(I am not quite is a:b=3:2 = a/b:3/2 or it was meant to be that way)

Since $xy=1$ it is $x^2+y^2=2xy$, which gives us $x^2-2xy+y^2=0\Leftrightarrow (x-y)^2=0$
This means, it has to be $x=y$. From the condition $xy=1$ we deduce $x^2=1\Leftrightarrow x=y=\pm 1$, which gives the only two solution $(1,1), (-1,-1)$.
