For the below questions, I understand how to find the different values of $a$ when looking for a unique solution for each, but I do not understand the second part on pairs of $a$ and $b$ to find infinite solutions. I know on a line graph the same point of intersection may also appear in the case of the lines lieing on top of each other (infinite). Other than being able to put these systems in matrix form, it seems unclear the fixed route to take rather than guessing. For example, one pair for System A would be (2,2), but I am unsure why this is the case and so I am unable to work out the others.
"Consider each of the following systems of equations with unknowns $x$, $y$. For which values of a does each system have a unique solution? For which pairs of values (a, b) does each system have an infinite number of solutions?"
System A: $$\begin{align*} x - ay &= 1\\ ax - 4y &= b. \end{align*}$$
System B: $$\begin{align*} ax + 3y &= 2\\ 12x + ay&= b \end{align*}$$
System C: $$\begin{align*} x + ay &= 3\\ 2x + 5y &= b \end{align*}$$