Решите систему уравнений: x+y+z=2; x-y+z=6; x+y-z=-4.

\[\left\{ \begin{matrix} x + y + z = 2\ \ ( - ) \\ x - y + z = 6\ \ ( + ) \\ x + y - z = - 4\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow 2y = - 4\]

\[\text{\ \ \ \ \ \ \ \ \ \ }\overline{\ \ \ \ \ \ \ \ \ \ 2x = 2\ \ \ \ \ }\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 1\]

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

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

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

\[Ответ:\ \ (1;\ - 2;3).\]