If 0.4x + 0.3y = 2.3 and 2.5x - 2y = -5, then the value of xy is :

1. 10

2. 12

3. 2.4

4. 1.2

Given,

0.4x + 0.3y = 2.3 and 2.5x - 2y = -5

Solving first equation,

⇒ 0.4x + 0.3y = 2.3

⇒ 10(0.4x + 0.3y = 2.3)     [Multiplying both sides by 10]

⇒ 4x + 3y = 23

⇒ 4x = 23 - 3y

⇒ x = $\dfrac{23 - 3y}{4}$     ….(1)

⇒ 2.5x - 2y = -5     ….(2)

Substituting value of x from equation (1) in 2.5x - 2y = -5, we get :

$\Rightarrow 2.5 \Big(\dfrac{23 - 3y}{4}\Big) - 2y = -5 \\[1em] \Rightarrow \dfrac{57.5 - 7.5y}{4} - 2y = -5 \\[1em] \Rightarrow \dfrac{57.5 - 7.5y - 8y}{4} = -5 \\[1em] \Rightarrow 57.5 - 15.5y = -5 \times 4 \\[1em] \Rightarrow 57.5 - 15.5y = -20 \\[1em] \Rightarrow -15.5y = -20 - 57.5 \\[1em] \Rightarrow -15.5y = -77.5 \\[1em] \Rightarrow y = \dfrac{-77.5}{-15.5} = 5.$

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

$\Rightarrow x = \dfrac{23 - 3y}{4} \\[1em] \Rightarrow x = \dfrac{23 - 3 \times 5}{4} \\[1em] \Rightarrow x = \dfrac{23 - 15}{4} \\[1em] \Rightarrow x = \dfrac{8}{4} = 2.$

x = 2 and y = 5.

xy = 10.

Hence, option 1 is the correct option.