Example 4: Let $\overline{2 x 3}+326=\overline{5 y 9}$, and $9 \mid \overline{5 y 9}$. Find $x+y$.

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Solve: 
$$
9|\overline{5 y 9} \Rightarrow 9|(5+y+9) \Rightarrow 9 \mid(5+y) \text {. }
$$

But $0 \leqslant y \leqslant 9$, then $y=4$.
$$
\begin{array}{l}
\text { Hence } \overline{2 x 3}+326=549 \Rightarrow \overline{2 x 3}=223 \\
\Rightarrow x=2 \Rightarrow x+y=6 .
\end{array}
$$