The system of equations $2x+6y+11=0$, $6y-18z+1=0, 6x+20y-6z+3=0$,

$$\begin{gathered} Augmented matrix \left[AD\right]=\left[\begin{array}{cccc}2& 6& 0& -11\\ 0& 6& -18& -1\\ 6& 20& -6& -3\end{array}\right] \\ R_3\to R_3-3 R_1 \\ ~\left[\begin{array}{cccc}1& 6& 0& 11\\ 0& 6& -18& -1\\ 0& 2& -6& 30\end{array}\right] \\ R_3\to 3R_3-R_2 \\ ~\left[\begin{array}{cccc}1& 6& 0& 11\\ 0& 6& -18& -1\\ 0& 0& 0& 91\end{array}\right] \\ Here rankA=2 and rank\left[AD\right]=3 \\ \Rightarrow rankA\ne rank\left[AD\right] \\ \Rightarrow The given system has no solution \end{gathered}$$