Solve the first and last equation for y.

From the first equation:

From the last equation:

Either or . If then implies , so the solution is nontrivial (although there are an infinite number of solutions where ).

Next, suppose and . Then plug in what you know into the second equation:

If , then , and this solution is trivial. So, suppose . Then multiply both sides by . Hence . Solve this quadratic: . So . So, you get or .

Hence, the three values for that give nontrivial solutions for the system are . Note that for any of those three values for , there are an infinite number of solutions for .