Hệ phương trình

C

- Hướng dẫn giải

$$\begin{gathered} \iff \left\{\begin{array}{c}2x-5y+z=10\\ x+2y-3z=10\\ 5y-z=-6\end{array}\right.\stackrel{\left(1\right)+\left(3\right)}{\to }\left\{\begin{array}{c}2x-5y+z=10\\ x+2y-3z=10\\ 2x=4\end{array}\right.\iff \left\{\begin{array}{c}4-5y+z=10\\ \begin{array}{l}2+2y-3z=10\\ x=2\end{array}\end{array}\right. \\ \iff \left\{\begin{array}{l}\begin{array}{c}-5y+z=6\\ \begin{array}{l}2y-3z=8\\ x=2\end{array}\end{array}\end{array}\right.\iff \left\{\begin{array}{c}\begin{array}{c}-15y+3z=18\\ 2y-3z=8\\ x=2\end{array}\end{array}\right.\iff \left\{\begin{array}{l}\begin{array}{c}-13y=26\\ 2y-3z=8\\ x=2\end{array}\end{array}\right.\iff \left\{\begin{array}{c}y=-2\\ z=-4\\ x=2\end{array}\right. \end{gathered}$$

Vậy nghiệm của hệ phương trình đã cho là ( 2; -2; -4).

Chọn C,