Решите систему уравнений: x+3y-z=4; 3x-y+2z=7; -x+5y-4z=-3.

\[\left\{ \begin{matrix} x + 3y - z = 4\ \ \ | \cdot 2 \\ 3x - y + 2z = 7\ \ \ \ \ \ \ \\ - x + 5y - 4z = - 3\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2x + 6y - 2z = 8\ \ \ \ ( - ) \\ 3x - y + 2z = 7\ \ \ \ \ ( - )\ \\ - x + 5y - 4z = - 3\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\text{\ \ \ }\overline{\ \ \ \ \ \ \ \ \ \ \ \ 2y = 4\ \ \ \ \ \ \ \ \ \ \ }\text{\ \ }\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ y = 2\]

\[\left\{ \begin{matrix} y = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x - z = - 2\ \ \ \ \ \ \ \ \\ - x - 4z = - 13 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ z = x + 2\ \ \ \ \ \ \ \ \ \ \ \\ - x = 4z - 13^{*} \\ \end{matrix} \right.\ \]

\[\ \ \ \ x + 4x = 5\]

\[\ \ \ \ \ 5x = 5\]

\[\ \ \ \ \ \ \ x = 1\]

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

\[Ответ:\ \ (1;2;3).\]