Решите систему уравнений: 6=3(x+y); 6-5(x-y)=8x-2y.

\[\left\{ \begin{matrix} 6 = 3 \cdot (x + y)\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 6 - 5 \cdot (x - y) = 8x - 2y \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x + y = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 6 - 5x + 5y - 8x + 2y = 0 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x + y = 2\ \ \ \ \ \ \ \ \ \ \ \ \\ - 13x + 7y = - 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 2 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - 13 \cdot (2 - y) + 7y = - 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[- 26 + 13y + 7y = - 6\]

\[20y = - 6 + 26\]

\[20y = 20\]

\[y = 1.\]

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

\[Ответ:(1;1).\]