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 2x2y2 = 1 and x2 = −1. You can pretend the variables are x2 and y2 and solve just like a linear system, getting x2 = −1 and y2 = −3. Now there are two possibilities for x, i and −i, and two for y, √3i and −√3i. So there are four possible solutions, once we account for all the possible combinations of x and y: {(−i, √3i), (−i, −√3i), (i, √3i), (i, −√3i)}.

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