Решите систему уравнений x-2y=1; xy+y=12.

Ответ:

\[\left\{ \begin{matrix} x - 2y = 1\ \ \\ xy + y = 12 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x = 2y + 1\ \ \ \ \ \ \\ y(x + 1) = 12 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 2y + 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y(2y + 1 + 1) = 12 \\ \end{matrix} \right.\ \]

\[2y^{2} + 2y - 12 = 0\ \ \ \ \ |\ :2\]

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

\[y_{1} + y_{2} = - 1;\ \ \ \ y_{1} \cdot y_{2} = - 6\]

\[y_{1} = - 3;\ \ \ y_{2} = 2.\]

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

\[Ответ:( - 5;\ - 3);(5;2).\]