\[\boxed{\text{496\ (496).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\boxed{\text{496.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ \left\{ \begin{matrix} x + y + xy = 5\ \ \\ xy + x - y = 13 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 2y = - 8\ \ \ \ \ \ \ \ \ \ \ \ \\ x + y + xy = 5 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = - 4\ \ \ \ \ \ \ \ \ \ \ \ \ \\ x - 4 - 4x = 5 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow y = - 4,\ \ x = - 3.\]
\[Ответ:( - 3;\ - 4).\]
\[\textbf{б)}\ \left\{ \begin{matrix} x + xy + y = 10\ \\ xy - 2x - 2y = 2 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 2x + 2xy + 2y = 20 \\ xy - 2x - 2y = 2\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 3xy = 22\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ xy - 2x - 2y = 2 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = \frac{22}{3y}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \frac{22}{3y} - \frac{44}{3y} - 2y - 2 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = \frac{22}{3y}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 11y - 22 - 3y^{2} - 3y = 0 \\ \end{matrix} \right.\ \]
\[3y^{2} - 8y + 22 = 0\]
\[D = 16 - 3 \cdot 22 < 0 \Longrightarrow\]
\[\Longrightarrow корней\ нет.\]
\[Ответ:корней\ нет.\]