Решите систему уравнений: x-2y-3z=0; 3x+2y+z=2; 2x+2y-5z=-5.

\[\left\{ \begin{matrix} x - 2y - 3z = 0\ \ \ \ \ \ \ \ \ ( + ) \\ 3x + 2y + z = 2\ \ \ \ \ \ \ \ ( - )\ \\ 2x + 2y - 5z = - 5\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} x + 6z = 7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - 2y - 9z = - 7\ \ \ \ \ \ \ \ \ \\ 4x - 2z = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ }\]

\[\left\{ \begin{matrix} x = 7 - 6z\ \ \ \ \ \ \ \ \\ 2y + 9z = 7\ \ \ \ \ \ \ \\ 4x - 2z = 2\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[4 \cdot (7 - 6z) - 2z = 2\]

\[28 - 24z - 2z = 2\]

\[26z = 26\]

\[z = 1\]

\[\left\{ \begin{matrix} z = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = 7 - 6 \cdot 1\ \ \ \ \ \ \ \ \ \ \ \\ 2y = 7 - 9 \bullet 1\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ }\]