Solution of equations $\dfrac{x}{2} - \dfrac{y}{3} = 0 \text{ and } \dfrac{x}{2} + \dfrac{y}{3} = 6$ is :

1. x = 6, y = -9

2. x = 6, y = 9

3. x = -6, y = -9

4. x = -6, y = 9

Given,

Equations :

$\Rightarrow \dfrac{x}{2} - \dfrac{y}{3} = 0 ……….(1) \\[1em] \Rightarrow \dfrac{x}{2} + \dfrac{y}{3} = 6 ……….(2)$

Adding equations (1) and (2), we get :

$\Rightarrow \dfrac{x}{2} - \dfrac{y}{3} + \dfrac{x}{2} + \dfrac{y}{3} = 0 + 6 \\[1em] \Rightarrow \dfrac{2x}{2} = 6 \\[1em] \Rightarrow x = 6.$

Substituting value of x in equation (1), we get :

$\Rightarrow \dfrac{6}{2} - \dfrac{y}{3} = 0 ……….(1) \\[1em] \Rightarrow \dfrac{6}{2} = \dfrac{y}{3} \\[1em] \Rightarrow \dfrac{y}{3} = 3 \\[1em] \Rightarrow y = 9.$

Hence, Option 2 is the correct option.