Решите в целых числах уравнение 2xy-x-4y=9.

\[2xy + x - 4y = 9\]

\[2y(x - 2) + (x - 2) = 7\]

\[(x - 2)(2y + 1) = 7\]

\[1)\ \left\{ \begin{matrix} x - 2 = 7\ \ \\ 2y + 1 = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 9 \\ y = 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[2)\ \left\{ \begin{matrix} x - 2 = 1\ \ \ \\ 2y + 1 = 7 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 3 \\ y = 3 \\ \end{matrix} \right.\ \]

\[3)\ \left\{ \begin{matrix} x - 2 = - 7 \\ 2y + 1 = 1\ \\ \end{matrix}\ \right.\ \text{\ \ \ }\left\{ \begin{matrix} x = - 5 \\ y = - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[4)\ \left\{ \begin{matrix} x - 2 = - 1\ \ \\ 2y + 1 = - 7 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 1\ \ \ \\ y = - 4 \\ \end{matrix} \right.\ \]

\[Ответ:(9;0);\ \ (3;3);\ \ ( - 5; - 1);\ \ \]

\[(1; - 4).\]