Решите в целых числах уравнение 2xy-x+6y=8.

\[2xy - x + 6y = 8\]

\[2y(x + 3) - (x + 3) = 5\]

\[(x + 3)(2y - 1) = 5\]

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

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

\[3)\ \left\{ \begin{matrix} x + 3 = - 5\ \ \\ 2y - 1 = - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x = - 8 \\ y = 0\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\ 4)\ \left\{ \begin{matrix} x + 3 = - 1\ \ \\ 2y - 1 = - 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x = - 4 \\ y = - 2 \\ \end{matrix} \right.\ \]

\[Ответ:\ (2;1);\ ( - 2;3);\ \ ( - 8;0);\ \ \]

\[( - 4;\ - 2).\]