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 .