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

Ответ:

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

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

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

\[\left\{ \begin{matrix} 4x + y = 5\ \ \ \ \ \ | \cdot 2 \\ - x - 2y = 11\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} 8x + 2y = 10\ \ \ (1) \\ - x - 2y = 11\ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) + (2) \Longrightarrow 7x = 21,\ \ x = 3.\]

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

\[Ответ:(3;\ - 7).\]