Найдите решение системы: x-y-z=0; x+y-z=6; x+y+z=8.

\[\left\{ \begin{matrix}
x - y - z = 0 \\
x + y - z = 6 \\
x + y + z = 8 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
x = y + z\ \ \ \ \ \ \ \ \ \\
x + x = 8\ \ \ \ \ \ \ \ \\
y - z = 6 - x \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
2x = 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
y + z = x\ \ \ \ \ \ \ \ \ \\
y - z = 6 - x \\
\end{matrix} \right.\ \]

\[\ \left\{ \begin{matrix}
x = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
y + z = 4\ \ \ \ \ \ \ \ \\
y - z = 6 - 4 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
x = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
y + z = 4\ \ (1) \\
y - z = 2\ \ (2) \\
\end{matrix} \right.\ \]

\[2y = 6\ \]

\[y = 3\]

\[\ \left\{ \begin{matrix}
x = 4\ \ \ \ \ \ \ \ \ \ \\
y = 3\ \ \ \ \ \ \ \ \ \\
y + z = 4 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
x = 4\ \ \ \ \ \ \ \ \ \\
y = 3\ \ \ \ \ \ \ \ \ \\
z = 4 - y \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
x = 4\ \ \ \ \ \ \ \ \\
y = 3\ \ \ \ \ \ \ \\
z = 4 - 3 \\
\end{matrix} \right.\ \ \]

\[\left\{ \begin{matrix}
x = 4 \\
y = 3 \\
z = 1 \\
\end{matrix} \right.\ \ \]

\[Ответ:(4;3;1).\]