Решите систему уравнений y^2-xy=33; x-y=11.

Ответ:

\[\left\{ \begin{matrix} y^{2} - xy = 33 \\ x - y = 11\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 11 + y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y^{2} - y(11 + y) = 33 \\ \end{matrix} \right.\ \]

\[y^{2} - 11y - y^{2} = 33\]

\[- 11y = 33\]

\[y = - 3.\]

\[\left\{ \begin{matrix} y = - 3\ \ \ \ \ \ \ \ \ \\ x = 11 - 3\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} y = - 3 \\ x = 8\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(8; - 3).\]