a) \(\left\{ \begin{array}{l}x + 2y - 3z = 2\\2x + 7y + z = 5\\ - 3x + 3y - 2z = - 7\end{array} \right.\)\( \Leftrightarrow \left\{ \begin{array}{l}x + 2y - 3z = 2\\3y + 7z = 1\\ - 32z = - 4\end{array} \right.\)\( \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{x = \dfrac{{55}}{{24}}}\\{y = \dfrac{1}{{24}}}\\{z = \dfrac{1}{8}}\end{array}} \right.\)
Đáp số:\((x;y;z) = (\dfrac{{55}}{{24}};\dfrac{1}{{24}};\dfrac{1}{8})\).
b) \(\left\{ \begin{array}{l} - x - 3y + 4z = 3\\3x + 4y - 2z = 5\\2x + y + 2z = 4\end{array} \right.\)\( \Leftrightarrow \left\{ \begin{array}{l} - x - 2y + 4z = 3\\ - 5y + 10z = 14\\ - 5y + 10z = 10\end{array} \right.\)\( \Leftrightarrow \left\{ \begin{array}{l} - x - 3y + 4z = 3\\ - 5y + 10z = 14\\0y + 0z = - 4\end{array} \right.\)
Phương trình cuối vô nghiệm, suy ra hệ phương trình đã cho vô nghiệm.
