The solution of 0.4x + 3y = 1.2 and 7x - 2y = $\dfrac{17}{6}$ is :

1. $x = \dfrac{1}{3}, y = \dfrac{1}{2}$

2. $x = \dfrac{1}{2}, y = \dfrac{1}{3}$

3. $x = \dfrac{1}{3}, y = 1$

4. $x = 0, y = \dfrac{1}{2}$

Given,

Equations: 0.4x + 3y = 1.2 and 7x - 2y = $\dfrac{17}{6}$

Solving first equation,

⇒ 0.4x + 3y = 1.2

Multiplying both sides of the equation by 10,

⇒ 10(0.4x + 3y) = 10 × 1.2

⇒ 4x + 30y = 12

⇒ 4x = 12 - 30y

⇒ x = $\dfrac{12 - 30y}{4}$     …….(1)

⇒ 7x - 2y = $\dfrac{17}{6}$     …….(2)

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

$\Rightarrow 7 \Big(\dfrac{12 - 30y}{4}\Big) - 2y = \dfrac{17}{6} \\[1em] \Rightarrow \dfrac{84 - 210y}{4} - 2y = \dfrac{17}{6} \\[1em] \Rightarrow \dfrac{84 - 210y - 8y}{4} = \dfrac{17}{6} \\[1em] \Rightarrow 84 - 218y = 4 \times \dfrac{17}{6} \\[1em] \Rightarrow 84 - 218y = 2 \times \dfrac{17}{3} \\[1em] \Rightarrow 3(84 - 218y) = 17 \times 2 \\[1em] \Rightarrow 252 - 654y = 34 \\[1em] \Rightarrow 654y = 252 - 34 \\[1em] \Rightarrow 654y = 218 \\[1em] \Rightarrow y = \dfrac{218}{654} \\[1em] \Rightarrow y = \dfrac{1}{3}.$

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

$\Rightarrow x = \dfrac{12 - 30y}{4} \\[1em] \Rightarrow x = \dfrac{12 - 30 \times \dfrac{1}{3}}{4} \\[1em] \Rightarrow x = \dfrac{12 - 10}{4} \\[1em] \Rightarrow x = \dfrac{2}{4} = \dfrac{1}{2}.$

Hence, option 2 is the correct option.