Решите систему уравнений: 9x+2y=16; 3x-5y=11.

Ответ:

\[\left\{ \begin{matrix} 9x + 2y = 16\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x - 5y = 11\ \ \ | \cdot ( - 3) \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 9x + 2y = 16\ \ \ \ \ \ \ \ \ \ \ \ (1) \\ - 9x + 15y = - 33\ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) + (2) \Longrightarrow 17y = - 17\]

\[\left\{ \begin{matrix} 17y = - 17\ \ \ \ \ \\ 9x + 2y = 16 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = - 1\ \ \ \ \ \ \ \ \ \ \ \ \\ 9x = 16 - 2y \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = \frac{16}{9} - \frac{2}{9} \cdot ( - 1) \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

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

\[Ответ:(2; - 1).\]