Solve the following pair of linear equations by the substitution method.

0.2x + 0.3y = 1.3 and 0.4x + 0.5y = 2.3

Given,

0.2x + 0.3y = 1.3 …………(1)

0.4x + 0.5y = 2.3 …………(2)

Solving equation (1),

⇒ 0.2x + 0.3y = 1.3

⇒ 0.2x = 1.3 - 0.3y

⇒ x = $\dfrac{1.3 - 0.3y}{0.2}$ …………(3)

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

$\Rightarrow 0.4 \times \Big(\dfrac{1.3 - 0.3y}{0.2}\Big) + 0.5y = 2.3 \\[1em] \Rightarrow 2(1.3 - 0.3y) + 0.5y = 2.3 \\[1em] \Rightarrow 2.6 - 0.6y + 0.5y = 2.3 \\[1em] \Rightarrow 2.6 - 0.1y = 2.3 \\[1em] \Rightarrow 0.1y = 2.6 - 2.3 \\[1em] \Rightarrow 0.1y = 0.3 \\[1em] \Rightarrow y = \dfrac{0.3}{0.1} = 3.$

Substituting value of y in equation (3), we get :

⇒ x = $\dfrac{1.3 - 0.3 \times 3}{0.2}$

⇒ x = $\dfrac{1.3 - 0.9}{0.2} = \dfrac{0.4}{0.2}$ = 2.

Hence, x = 2 and y = 3.