Question 80
Find all triples of real numbers $(x, y, z)$ that satisfy the system of equations
$$
\begin{aligned}
x^2 + y^2 + 4z^2 &= 6y - 4, \\
2xy - 4xz + 4yz &= y^2 + 5.
\end{aligned}
$$
$$
\begin{aligned}
x^2 + y^2 + 4z^2 &= 6y - 4, \\
2xy - 4xz + 4yz &= y^2 + 5.
\end{aligned}
$$