Question 122
Find all ordered triples $(x, y, z)$ of real numbers which satisfy the following system of equations:
$$
\left\{\begin{array}{l}
x y = z - x - y \\
x z = y - x - z \\
y z = x - y - z
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
x y = z - x - y \\
x z = y - x - z \\
y z = x - y - z
\end{array}\right.
$$