Решите систему уравнений 2*(3x-y)-5=2x-3y; 5-(x-2y)=4y+16.

Ответ:

\[\left\{ \begin{matrix} 2 \cdot (3x - y) - 5 = 2x - 3y \\ 5 - (x - 2y) = 4y + 16\ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 6x - 2y - 5 = 2x - 3y \\ 5 - x + 2y = 4y + 16\ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 4x + y = 5\ \ \ \ \ \ \\ x + 2y = - 11 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

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

\[\left\{ \begin{matrix} y = 5 - 4x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x + 10 - 8x = - 11 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 5 - 4x\ \ \\ - 7x = - 21 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = 5 - 4 \cdot 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 3\ \ \ \\ y = - 7 \\ \end{matrix} \right.\ \]

\[Ответ:(3;\ - 7).\]