Решите систему уравнений: 3(5x+3y)-6=2x+11; 4x-15=11-2(4x-y).

Ответ:

\[\left\{ \begin{matrix} 3 \cdot (5x + 3y) - 6 = 2x + 11 \\ 4x - 15 = 11 - 2 \cdot (4x - y) \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 15x + 9y - 6 - 2x = 11\ \ \ \\ 4x - 15 = 11 - 8x + 2y\ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 13x + 9y = 17\ \ \ \ \ \ \ \ \ \ \\ 12x - 2y = 26\ \ \ | \cdot \frac{9}{2} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 13x + 9y = 17\ \ \ \\ 54x - 9y = 117 \\ \end{matrix} \right.\ ( + )\]

\[67x = 134\]

\[x = 2.\]

\[\left\{ \begin{matrix} y = 6x - 13 \\ x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 12 - 13 \\ x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]

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

\[Ответ:(2;\ - 1).\]