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

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

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

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

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

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

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

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

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

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

\[Ответ:(5;3).\]