Найдите решение системы уравнений: x+y=2; y+z=4; z+x=6.

\[\left\{ \begin{matrix}
x + y = 2 \\
y + z = 4 \\
z + x = 6 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

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

\[\left\{ \begin{matrix}
y = 2 - x\ \ \ \ \ \ \\
z = 6 - x\ \ \ \ \ \ \\
- 2x = 4 - 8 \\
\end{matrix} \right.\ \]

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

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

\[\left\{ \begin{matrix}
x = 2 \\
y = 0 \\
z = 4 \\
\end{matrix} \right.\ \]

\[Ответ:(2;0;4).\]