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

Ответ:

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

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

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

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

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

\[\left\{ \begin{matrix} x = - 2 \\ y = - 4 \\ z = 7\ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:( - 2;\ - 4;7).\]