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

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

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

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

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

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

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

\[Ответ:(2;0;4).\]