What is the easiest proof to prove that all lines of the form $(a+2)x - (a+1)y - 2a - 3 = 0$ pass through some common point, where $a$ is a real number, and how to find that point. I tried taking $a_1$ and $a_2$ and somehow to prove it with determinants, but I got stuck.
I would choose values for $a$ that eliminate one variable. If $a=-2$ you get an equation in $y$ only. If $a=-1$, you get an equation in $x$ only. The solutions to these two equations are the coordinates you want.