Use the ratio test to say how many solutions each pair has…

Step 1. (a) The ratios are $\dfrac{5}{10}$, $\dfrac{2}{4}$ and $\dfrac{-9}{-18}$, all $\dfrac{1}{2}$. The lines coincide: infinitely many solutions.

Step 2. (b) The ratios are $\dfrac{2}{6} = \dfrac{1}{3}$, $\dfrac{-3}{-9} = \dfrac{1}{3}$ and $\dfrac{-4}{-5} = \dfrac{4}{5}$. The first two are equal and the third differs: parallel lines, no solution.

Step 3. (c) The first two ratios are $\dfrac{1}{3}$ and $\dfrac{4}{2} = 2$. They differ, so the lines cross: exactly one solution.