Positive integers $x, y, z \leq 100$ satisfy the following equations:
\[ \begin{align*}
1099x + 901y + 1110z &= 59800 \\
109x + 991y + 101z &= 44556
\end{align*} \]
Compute $10000x + 100y + z$.

Let's think step by step and output the final answer within \boxed{}.
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