The problem is as follows:

Sometimes we may need to solve a system of equations that isn't linear, but wants to be. With this in mind, solve the following system of nonlinear equations for x, y, and z.

xz + yz + xy = -1

xz - yz + 2xy = 5

xz - 2yz + 2xy = 7

I put the equations into matrices and got so far as xz = 20, -yz = -5, -xy = -16. But now I don't know where to go... any help would be much appreciated!