Решите систему уравнений: 2xy-x=9; 2xy+5y=22.

Ответ:

\[\left\{ \begin{matrix} 2xy - x = 9\ \ \ \ \ \\ 2xy + 5y = 22 \\ \end{matrix}\text{\ \ } \right.\ ( - )\text{\ \ }\]

\[\left\{ \begin{matrix} 5y + x = 13\ \ \ \ \\ 2xy + 5y = 22 \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x = 13 - 5y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2y(13 - 5y) + 5y = 22 \\ \end{matrix} \right.\ \]

\[26y - 10y^{2} + 5y - 22 = 0\]

\[- 10y^{2} + 31y - 22 = 0\]

\[D = 961 - 880 = 81\]

\[y = \frac{- 31 + 9}{- 20} = 1,\ 1;\ \ \ \ \ \ \ \ \ \ \ \]

\[y = \frac{- 31 - 9}{- 20} = 2\]

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

\[\left\{ \begin{matrix} x = 7,\ 5 \\ y = 1,1 \\ \end{matrix} \right.\ \]

\[Ответ:(3;2);\ (7,5;1,1).\]