Find the values of the letters and give reasons for the steps involved. $12A+6AB=A09$

Solution: $12A+6AB=A09$
Here, we can see that , $A+B=9\to \left(1\right)$
$2+A=0\to \left(2\right)$
$1+6=A\to \left(3\right)$
From (2), we can see that possible values for $A$ is $8$ or $7$.
For $A$ to be $7$, $A+B$ should be greater that $9$ that is not possible from $\left(1\right)$.
So, value of $A$ is $8$.
From (1), we can see that if $A$ = $8$, then $B=9-8=1$
So, $A=8\text{and}B=1$