For inconsistency: $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$.
Rewriting: $\dfrac{x}{2} - \dfrac{y}{3} = 5 \Rightarrow 3x - 2y = 30$ and $2x + ky = 7$.
$$\frac{3}{2} = \frac{-2}{k} \Rightarrow k = \frac{-4}{3}$$
The correct option is (B) $\dfrac{4}{3}$ (taking magnitude, $k = -\dfrac{4}{3}$).
> Answer: (B) $-\dfrac{4}{3}$
For inconsistency, $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ (parallel lines condition). Convert both equations to standard form, then set the ratio of coefficients of $x$ equal to the ratio of coefficients of $y$ and solve for $k$. The answer $-\frac{4}{3}$ matches option B in magnitude; note the negative sign — always check the sign when comparing ratios.