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

Ответ:

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

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

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

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

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

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

\[Ответ:(1;\ - 2;2)\text{.\ }\]