Решите систему уравнений: (x-1)/3+(y-1)/3=2; (x-1)/2-(y-1)/6=5/3.

Ответ:

\[\left\{ \begin{matrix} \frac{x - 1}{3} + \frac{y - 1}{3} = 2\ \ \ | \cdot 3 \\ \frac{x - 1}{2} - \frac{y - 1}{6} = \frac{5}{3}\ \ \ \ | \cdot 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} x - 1 + y - 1 = 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3 \cdot (x - 1) - (y - 1) = 10 \\ \end{matrix} \right.\ \text{\ \ }\]

\[\ \left\{ \begin{matrix} x + y = 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x - 3 - y + 1 = 10 \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} x + y = 8\ \ \ \ \ \ \ \ (1) \\ 3x - y = 12\ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) + (2) \Longrightarrow 4x = 20\]

\[\left\{ \begin{matrix} 4x = 20\ \ \ \\ x + y = 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 5\ \ \ \ \ \ \ \ \ \\ y = 8 - x \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 5\ \ \ \ \ \ \ \ \\ y = 8 - 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 5 \\ y = 3 \\ \end{matrix} \right.\ \]

\[Ответ:(5;3).\]