The system of equations $x+2 y=3$ and $3 x+6 y=a-2$ has no solution

Given The system of equations $x+2 y=3$, $3 x+6 y=a-2$ has no solution. Since, we know that simultaneous linear equations $a_1 x+b_1 y=c_1$ and $a_2 x+b_2 y=c_2$ has no solution, if $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ Hence, from the given equations, $$ \begin{aligned} \frac{1}{3} & =\frac{2}{6} \neq \frac{3}{a-2} \\ \Rightarrow \quad \frac{1}{3} & =\frac{1}{3} \neq \frac{3}{a-2} \end{aligned} $$ To satisfy above condition, $a-2 \neq 9$ $$ \Rightarrow \quad a \neq 11 $$