Question 58
Compute the number of real solutions $(x, y, z, w)$ to the system of equations:
$$
\begin{array}{rlrl}
x & = z + w + z w x & z & = x + y + x y z \\
y & = w + x + w x y & w & = y + z + y z w
\end{array}
$$
$$
\begin{array}{rlrl}
x & = z + w + z w x & z & = x + y + x y z \\
y & = w + x + w x y & w & = y + z + y z w
\end{array}
$$