Question 96
Find all real solutions of the system
$$
\begin{cases}
|x + y + z| = 1 \\
|x| + |y| + |z| = 1 \\
|x - y| + |y - z| + |z - x| = 2.
\end{cases}
$$
$$
\begin{cases}
|x + y + z| = 1 \\
|x| + |y| + |z| = 1 \\
|x - y| + |y - z| + |z - x| = 2.
\end{cases}
$$