For which value of k does the pair 3x + ky = 7 and 6x + 15y = 5 have no solution?

Step 1. Equal first two ratios. $\dfrac{3}{6} = \dfrac{k}{15}$, so $k = 7.5$.

Step 2. Check the third ratio. $\dfrac{7}{5}$ is not $\dfrac{1}{2}$, so the lines are parallel and the pair has no solution.

Step 3. The same line. We need $\dfrac{7}{c} = \dfrac{1}{2}$, so $c = 14$.