Найдите решение системы уравнений: x+y=1-z; x-y=3; z=2x.

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

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

\[\left\{ \begin{matrix}
z = 2x\ \ \ \ \ \ \ \ \ \ \\
y = x - 3\ \ \ \ \ \\
2x + 2x = 4 \\
\end{matrix} \right.\ \]

\[\left\{ \begin{matrix}
z = 2x\ \ \ \ \ \ \\
y = x - 3 \\
4x = 4\ \ \ \ \ \ \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

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

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

\[Ответ:(1;\ - 2;2)\text{.\ }\]