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

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

\[\text{\ \ \ \ \ \ \ }\overline{\ \ \ \ \ \ \ \ - 2y = - 4\ \ \ }\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ y = 2\]

\[\left\{ \begin{matrix} 2x - 2y + 2z = 12\ \ \ \ \ \ \\ x - y - z = 2\ \ \ ( - )( + ) \\ x + y - z = 6\ \ \ ( - )( + ) \\ \end{matrix} \right.\ \]

\[( - ) - 2y + 4z = 4\ \ \ |\ :2\]

\[( + )\ \ \ 4x - 2y = 20\ \ \ |\ :2\]

\[\left\{ \begin{matrix} - y + 2z = 2 \\ 2x - y = 10\ \\ y = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 2\ \ \ \ \ \ \ \ \ \ \ \ \\ 2x - 2 = 10 \\ - 2 + 2z = 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

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

\[Ответ:(6;2;2).\]