Ta có:
\(\begin{array}{l}\;\;\;\;\left\{ \begin{array}{l}3x + 5y - z = 9\\x + 3y + 2z = 1\\5x - 2y - 3z = - 3\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}6x + 10y - 2z = 18\\x + 3y + 2z = 1\\5x - 2y - 3z = - 3\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}7x + 13 = 19\\x + 3y + 2z = 1\\5x - 2y - 3z = - 3\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}7x + 13y = 19\\3x + 9y + 6z = 3\\10x - 4y - 6z = - 6\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}7x + 13y = 19\\13x + 5y = - 3\\10x - 4y - 6z = - 6\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}91x + 169y = 247\\91x + 35y = - 21\\10x - 4y - 6z = - 6\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}134y = 268\\91x + 35y = - 21\\10x - 4y - 6z = - 6\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}x = - 1\\y = 2\\x = - 2\end{array} \right..\end{array}\)
Vậy hệ phương trình có nghiệm \((x; y; z) = (-1; 2; -2).\)
