Solve $5a^2 - 4ab - b^2 + 9 = 0$, $ - 21a^2 - 10ab + 40a - b^2 + 8b - 12 = 0$ 
Solve $\left\{\begin{matrix} 5a^2 - 4ab - b^2 + 9 = 0\\ - 21a^2 - 10ab + 40a - b^2 + 8b - 12 = 0. \end{matrix}\right.$

I know that we can use quadratic equation twice, but then we'll get some very complicated steps. Are there any elegant way to solve this? Thank you.

Note that
\begin{equation*}
4(5a^2 - 4ab - b^2 + 9)  - 9(-21a^2-10ab+40a-b^2+8b-12) = (19a+5b-12)(11a+b-12).
\end{equation*}
