Решите систему уравнений 6x+11y=107; 5x-2y=11.

Ответ:

\[\left\{ \begin{matrix} 6x + 11y = 107\ \ | \cdot 2 \\ 5x - 2y = 11\ \ \ \ \ | \cdot 11 \\ \end{matrix} \right.\ \ \]

\[\left\{ \begin{matrix} 12x + 22y = 214 \\ 55x - 22y = 121 \\ \end{matrix} \right.\ \ ( + )\]

\[67x = 335\]

\[x = 5.\]

\[\left\{ \begin{matrix} 2y = 5x - 11 \\ x = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} 2y = 5 \cdot 5 - 11 \\ x = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 5\ \ \ \ \ \\ 2y = 14 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 5 \\ y = 7 \\ \end{matrix} \right.\ \]

\[Ответ:(5;7).\]