Решите систему уравнений: 2(3x+2y)+9=4x+21; 2x+10=3-(6x+5y).

\[\left\{ \begin{matrix} 2 \cdot (3x + 2y) + 9 = 4x + 21 \\ 2x + 10 = 3 - (6x + 5y)\text{\ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 6x + 4y + 9 = 4x + 21 \\ 2x + 10 = 3 - 6x - 5y \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 6x - 4x + 4y = 21 - 9 \\ 2x + 6x + 5y = 3 - 10 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2x + 4y = 12\ \ |\ :2 \\ 8x + 5y = - 7\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x + 2y = 6\ \ \ \ \ \ \\ 8x + 5y = - 7 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 6 - 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 8 \cdot (6 - 2y) + 5y = - 7 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 6 - 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 48 - 16y + 5y = - 7 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 6 - 2y\ \ \ \ \\ - 11y = - 55 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = 6 - 2 \cdot 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 5\ \ \ \ \\ x = - 4 \\ \end{matrix} \right.\ \]

\[Ответ:( - 4;5).\]