Решите систему уравнений: 3(2x+y)-26=3x-2y; 15-(x-3y)=2x+5.

\[\left\{ \begin{matrix} 3 \cdot (2x + y) - 26 = 3x - 2y \\ 15 - (x - 3y) = 2x + 5\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 6x + 3y - 26 = 3x - 2y \\ 15 - x + 3y = 2x + 5\ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 6x - 3x + 3y + 2y = 26 \\ - x - 2x + 3y = 5 - 15\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 3x + 5y = 26\ \ \ \ \ \ \ \ \ \ (1) \\ - 3x + 3y = - 10\ \ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) + (2) \Longrightarrow 8y = 16,\ \ y = 2.\]

\[\left\{ \begin{matrix} y = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = \frac{26}{3} - \frac{5}{3}y \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = \frac{26}{3} - \frac{5}{3} \cdot 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = \frac{26}{3} - \frac{10}{3} = \frac{16}{3} = 5\frac{1}{3} \\ \end{matrix} \right.\ \]

\[Ответ:\left( 5\frac{1}{3};\ 2 \right)\text{.\ }\]