For infinitely many solutions: $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$
Here, $\dfrac{6}{36} = \dfrac{1}{6} = \dfrac{3k}{3}$, so $\dfrac{1}{6} = k$, giving $k = \dfrac{1}{6}$.
Answer: (B) $\dfrac{1}{6}$
For infinitely many solutions, the ratio condition $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ must hold. The coefficient ratio $\frac{6}{36}=\frac{1}{6}$ must equal $\frac{3k}{3}=k$, so $k=\frac{1}{6}$. Always rewrite equations in standard form before comparing ratios.