You may want to review solving linear systems first.

You can also sometimes solve systems where both equations are
quadratic. For example, suppose you're given
2*x*^{2} − *y*^{2} = 1
and *x*^{2} = −1. You can pretend the variables
are *x*^{2} and *y*^{2} and solve just
like a linear system, getting *x*^{2} = −1
and *y*^{2} = −3. Now there are two
possibilities for *x*, *i* and −*i*, and two
for *y*, √3*i* and −√3*i*. So
there are four possible solutions, once we account for all the
possible combinations of *x* and *y*: {(−*i*,
√3*i*), (−*i*, −√3*i*),
(*i*, √3*i*), (*i*,
−√3*i*)}.

Note that each choice for *x* can go with each choice
for *y*.