Solution of equations $\dfrac{x}{7} - \dfrac{y}{2} = 2 \text{ and } \dfrac{x - y}{3} = 3$ is :

1. x = 7, y = 2

2. x = -7, y = 2

3. x = -7, y = -2

4. x = 7, y = -2

Given, equations : $\dfrac{x}{7} - \dfrac{y}{2} = 2 \text{ and } \dfrac{x - y}{3} = 3$

Simplifying first equation :

$\Rightarrow \dfrac{x}{7} - \dfrac{y}{2} = 2 \\[1em] \Rightarrow \dfrac{2x - 7y}{14} = 2 \\[1em] \Rightarrow 2x - 7y = 28 \\[1em] \Rightarrow 2x - 7y - 28 = 0 \text{ ……..(1)}$

Simplifying second equation :

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

By cross-multiplication method :

$\Rightarrow \dfrac{x}{(-7) \times (-9) - (-1) \times (-28)} = \dfrac{y}{(-28) \times 1 - (-9) \times 2} = \dfrac{1}{2 \times (-1) - 1 \times (-7)} \\[1em] \Rightarrow \dfrac{x}{63 - 28} = \dfrac{y}{-28 - (-18)} = \dfrac{1}{-2 + 7} \\[1em] \Rightarrow \dfrac{x}{35} = \dfrac{y}{-10} = \dfrac{1}{5} \\[1em] \Rightarrow \dfrac{x}{35} = \dfrac{1}{5} \text{ and } \dfrac{y}{-10} = \dfrac{1}{5} \\[1em] \Rightarrow x = \dfrac{35}{5} \text{ and } y = \dfrac{-10}{5} \\[1em] \Rightarrow x = 7 \text{ and } y = -2.$

Hence, Option 4 is the correct option.