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

Ответ:

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

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

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

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

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

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

\[Ответ:(1;2;3).\]