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

Ответ:

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

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

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

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

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

\[\left\{ \begin{matrix} y = 2 \\ x = 4 \\ z = 5 \\ \end{matrix} \right.\ \]

\[Ответ:(4;2;5).\]