Question 8
Find all real numbers $x, y$ and $z$ that solve the system of equations $$
\begin{aligned}
x + y + 2z &= 0 \\
x y - z^{2} &= 0 \\
y^{2} + 5z + 6 &= 0
\end{aligned}
$$
\begin{aligned}
x + y + 2z &= 0 \\
x y - z^{2} &= 0 \\
y^{2} + 5z + 6 &= 0
\end{aligned}
$$