<s>[INST] 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.
 [/INST] $21a^2+10ab+b^2-10a-8b+12=0$
$(7a+b)(3a+b)-4(7a+b+3a+b)+12=0$
$(7a+b-4)(3a+b-4)=4--->(1)$
$5a^2-4ab-b^2=(5a+b)(a-b)=-9--->(2)$
If $7a+b-4=\frac 2 k, 3a+b-4=2k$, 
Express $a,b$ in terms of $k,$ replace their values in (2).
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