Example 1. Find a particular solution to $308 x+211 y=1$.

The above text is translated into English, preserving the original text's line breaks and format. Directly output the translation result.
Solution:
$2\left|\begin{array}{cc}308 & 211 \\ 211 & 194 \\ \hline 97 & 17 \\ 85 & 12 \\ 12 & -5 \\ 10 & 4 \\ -2 & 1\end{array}\right| 2$
\begin{tabular}{c|c|c|} 
& 308 & 211 \\
\hline-1 & 0 & 1 \\
-2 & 1 & -1 \\
-5 & -2 & 3 \\
-1 & 11 & -16 \\
-2 & -13 & 19 \\
-2 & 37 & -54
\end{tabular}
$$
-87 \mid 127 r_{\Delta}-1
$$
$x_{0}=-87, y_{0}=127$ is a particular solution.
Example 2. Find a particular solution to the equation $37 x-256 y=3$.
$\therefore(7,1)$ is a particular solution.
(Author's affiliation: Tianjin Wuyi Normal School)