Use the ratios, without solving, to find how many solutions each pair has.

Step 1. Pair (a). $\dfrac{1}{3}$, $\dfrac{4}{12} = \dfrac{1}{3}$, $\dfrac{5}{15} = \dfrac{1}{3}$. All equal: the same line, infinitely many solutions.

Step 2. Pair (b). $\dfrac{1}{3}$, $\dfrac{1}{3}$, $\dfrac{5}{9}$. The last differs: parallel lines, no solution.

Step 3. Pair (c). $\dfrac{1}{4}$ and $\dfrac{4}{1}$ differ: the lines cross, one solution. It is $(1, 1)$.