Решите в целых числах уравнение 2xy-x+4y=7.

\[2xy - x + 4y = 7\]

\[2y(x + 2) - (x + 2) = 5\]

\[(x + 2)(2y - 1) = 5\]

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

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

\[3)\ \left\{ \begin{matrix} x + 2 = - 5\ \ \ \\ 2y - 1 = - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = - 7 \\ y = 0\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\ \ 4)\ \left\{ \begin{matrix} x + 2 = - 1\ \ \ \\ 2y - 1 = - 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = - 2 \\ y = - 2 \\ \end{matrix} \right.\ \]

\[Ответ:(3;1);\ \ ( - 1;3);\ \ ( - 7;0);\ \]

\[\ ( - 3;\ - 2).\]