Найдите решение системы: x-y+z=2; x+y=3; z-y=1.

\[\left\{ \begin{matrix}
x - y + z = 2 \\
x + y = 3\ \ \ \ \ \ \ \\
z - y = 1\ \ \ \ \ \ \ \ \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
z - y = 1\ \ \ \ \ \ \ \ \\
x + z - y = 2 \\
x + y = 3\ \ \ \ \ \ \ \ \ \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
z - y = 1 \\
x + 1 = 2 \\
y = 3 - x \\
\end{matrix} \right.\ \ \]

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

\[\left\{ \begin{matrix}
x = 1\ \ \ \ \ \ \ \ \\
y = 2\ \ \ \ \ \ \ \\
z = 1 + 2 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
x = 1 \\
y = 2 \\
z = 3 \\
\end{matrix} \right.\ \]

\[Ответ:(1;2;3).\]