Question 41
Find all triples $(x, y, z)$ of real numbers that satisfy the system of equations
$$
\begin{cases} xy + x + y = z, \\ yz + y + z = x, \\ zx + z + x = y. \end{cases}
$$
$$
\begin{cases} xy + x + y = z, \\ yz + y + z = x, \\ zx + z + x = y. \end{cases}
$$