Compute the number of real solutions $(x,y,z,w)$ to the system of equations:
\begin{align*}
x &= z+w+zwx, \\ 
y &= w+x+wxy, \\
z &= x+y+xyz, \\
w &= y+z+yzw.
\end{align*}
Question:
Compute the number of real solutions $(x,y,z,w)$ to the system of equations:
\begin{align*}
x &= z+w+zwx, \\ 
y &= w+x+wxy, \\
z &= x+y+xyz, \\
w &= y+z+yzw.
\end{align*}
Answer:
Let's think step by step.

user
5
Compute the number of real solutions $(x,y,z,w)$ to the system of equations:
\begin{align*}
x &= z+w+zwx, \\ 
y &= w+x+wxy, \\
z &= x+y+xyz, \\
w &= y+z+yzw.
\end{align*}
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