Question 89
Let $n \in \mathbb{N}, n \ge 4$, and $A_n = \{1, 2, 3, \dots, n\}$. Find the number of solutions in the set $A_n \times A_n \times A_n \times A_n$ of the system
$$
\begin{cases}
x + z = 2y \\
y + t = 2z
\end{cases}
$$
$$
\begin{cases}
x + z = 2y \\
y + t = 2z
\end{cases}
$$