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

Ответ:

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

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

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

\[\left\{ \begin{matrix} 8x + 16y = 48 \\ 8x + 5y = - 7\ \ \\ \end{matrix} \right.\ \text{\ \ }( - )\]

\[11y = 55 \rightarrow y = 5.\]

\(\left\{ \begin{matrix} y = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x = 12 - 4y \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} y = 5\ \ \ \ \ \ \ \ \ \ \\ x = 6 - 2y \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} y = 5\ \ \ \\ x = - 4 \\ \end{matrix} \right.\ \)

\[Ответ:( - 4;\ 5).\]