9.1. For what values of the parameter $a$ do the equations $a x+a=7$ and $3 x-a=17$ have a common integer root?
Answer: $a=1$.

Solution. Solving these two equations as a system with unknowns $x$ and $a$, express $a$ from the second equation and substitute it into the first. We get the quadratic equation $3 x^{2}-14 x-24=0$. It has two roots: 6 and (-4/3). For the integer root $x=6$, the corresponding value of $a=3 x-17=1$.