Решите систему уравнений x-5y=3; xy+3y=11.

\[\left\{ \begin{matrix} x - 5y = 3\ \ \ \ \ \\ xy + 3y = 11 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 3 + 5y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (3 + 5y)y + 3y = 11 \\ \end{matrix} \right.\ \]

\[3y + 5y^{2} + 3y - 11 = 0\]

\[5y^{2} + 6y - 11 = 0\]

\[D = 9 + 55 = 64\]

\[y_{1} = \frac{- 3 + 8}{5} = 1;\ \ \]

\[y_{2} = \frac{- 3 - 8}{5} = - \frac{11}{5} = - 2,2\]

\[\left\{ \begin{matrix} y = 1 \\ x = 8 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = - 2,2 \\ x = - 8\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(8;1);( - 8;\ - 2,2).\]