Solution of equations $\dfrac{x + 8}{5} - \dfrac{2y - 4}{3} = 0$ and y - x = 3 is :

1. x = 2, y = 5

2. x = -2, y = 5

3. x = 2, y = -5

4. x = -2, y = -5

Given,

Equations :

$\Rightarrow \dfrac{x + 8}{5} - \dfrac{2y - 4}{3} = 0$ ……(1)

⇒ y - x = 3

⇒ y = x + 3 ………(2)

Substituting value of y from equation (2) in (1), we get :

$\Rightarrow \dfrac{x + 8}{5} - \dfrac{2(x + 3) - 4}{3} = 0 \\[1em] \Rightarrow \dfrac{x + 8}{5} - \dfrac{2x + 6 - 4}{3} = 0 \\[1em] \Rightarrow \dfrac{x + 8}{5} - \dfrac{2x + 2}{3} = 0 \\[1em] \Rightarrow \dfrac{3(x + 8) - 5(2x + 2)}{15} = 0 \\[1em] \Rightarrow 3x + 24 - 10x - 10 = 0 \\[1em] \Rightarrow -7x + 14 = 0 \\[1em] \Rightarrow 7x = 14 \\[1em] \Rightarrow x = \dfrac{14}{7} = 2.$

Substituting value of x in equation (2), we get :

⇒ y = x + 3 = 2 + 3 = 5.

Hence, Option 1 is the correct option.