Решите в целых числах уравнение 2xy+x-6y=10.

\[2xy + x - 6y = 10\]

\[2y(x - 3) + (x - 3) = 7\]

\[(x - 3)(2y + 1) = 7\]

\[1)\ \left\{ \begin{matrix} x - 3 = 7\ \ \\ 2y + 1 = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 10 \\ y = 0\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[2)\ \left\{ \begin{matrix} x - 3 = 1\ \ \ \\ 2y + 1 = 7 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 4 \\ y = 3 \\ \end{matrix} \right.\ \]

\[3)\ \left\{ \begin{matrix} x - 3 = - 7\ \ \\ 2y + 1 = - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x = - 4 \\ y = - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[4)\ \left\{ \begin{matrix} x - 3 = - 1\ \ \\ 2y + 1 = - 7 \\ \end{matrix} \right.\ \text{\ \ \ \ }\left\{ \begin{matrix} x = 2\ \ \ \\ y = - 4 \\ \end{matrix} \right.\ \]

\[Ответ:(10;0);\ \ \ (4;3);\ \ ( - 4; - 1);\ \ \]

\[(2; - 4).\]