Question

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

• A. x = 2, y = 3
• B. x = 2, y = -2
• C. x = 1, y = -3
• D. x = -2, y = -1

Answer 1

The correct option is A

x = 2, y = 3

0.2x + 0.3y = 1.3 ... (i)
0.4x + 0.5y = 2.3 ... (ii)
0.2x + 0.3y = 1.3
From equation (i), we get
0.2x = 1.3 - 0.3y
Dividing by 0.2, we get
$x=\frac{1.3}{0.2}-\frac{0.3}{0.2}$y
x = 6.5 - 1.5 y …(iii)
Substituting the value of x in equation (ii), we get,
$\Rightarrow$ 0.4x + 0.5y = 2.3
$\Rightarrow$ 0.4 $\times$ (6.5 - 1.5y) + 0.5y = 2.3
$\Rightarrow$ 2.6 - 0.6y + 0.5y = 2.3
$\Rightarrow$ -0.1y = 2.3 - 2.6
$\Rightarrow$ $y=\frac{-0.3}{-0.1}$
$\Rightarrow$ y = 3
Substituting the value in equation (iii) we get,
$\Rightarrow$ x = 6.5 - 1.5 y
$\Rightarrow$ x = 6.5 - 1.5(3)
$\Rightarrow$ x = 6.5 - 4.5
$\Rightarrow$ x = 2
$\therefore$ x = 2 and y = 3