Solve the following pair of linear equations by the substitution method.
$0.2 x + 0.3 y = 1.3$
$0.4 x + 0.5 y = 2.3$

(N/A) Given equations are:
$0.2 x + 0.3 y = 1.3$ $...(1)$
$0.4 x + 0.5 y = 2.3$ $...(2)$
From equation $(1)$,we express $x$ in terms of $y$:
$0.2 x = 1.3 - 0.3 y$
$x = \frac{1.3 - 0.3 y}{0.2}$ $...(3)$
Substituting the value of $x$ from equation $(3)$ into equation $(2)$:
$0.4 \left( \frac{1.3 - 0.3 y}{0.2} \right) + 0.5 y = 2.3$
$2(1.3 - 0.3 y) + 0.5 y = 2.3$
$2.6 - 0.6 y + 0.5 y = 2.3$
$2.6 - 0.1 y = 2.3$
$2.6 - 2.3 = 0.1 y$
$0.3 = 0.1 y$
$y = \frac{0.3}{0.1} = 3$
Now,substitute $y = 3$ into equation $(3)$:
$x = \frac{1.3 - 0.3(3)}{0.2}$
$x = \frac{1.3 - 0.9}{0.2}$
$x = \frac{0.4}{0.2} = 2$
Therefore,the solution is $x = 2$ and $y = 3$.