For all values of $a$ and $b$ the line $(a+2 b) x+(a-b) y+(a+5 b)=0$ passes through the point.
For all values of $a$ and $b$ the line $(a+2 b) x+(a-b) y+(a+5 b)=0$ passes through the point.
$(-1,2)$
$(2,-1)$
$(-2,1)$
$(1,-2)$
Solution
Let the line passes through a point whose coordinates are $(-2,1)$, then
$\begin{aligned}(a & +2 b)(-2)+(a-b)(1)+a+5 b \\ & =-2 a-4 b+a-b+a+5 b \\ & =-2 a-5 b+2 a+5 b \\ & =0\end{aligned}$
$\therefore$ Our assumption is true. The required point is $(-2,1)$