For what value of $k$ does the pair $2x + ky = 7$ and $6x + 15y = 11$ have no solution?

Explanation

1. 01

   No solution means parallel lines: $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.

2. 02

   $\frac{2}{6} = \frac{k}{15}$, so $k = \frac{15}{3} = 5$.

3. 03

   Check the constants: $\frac{7}{11} \neq \frac{1}{3}$, so the lines are parallel and distinct.