Question

Solve the following pair of linear equations by the substitution method.
$0.2x+0.3y=1.30.4x+0.5y=2.3$

Answer 1

0.2x+0.3y=1.3 ......(1)

0.4x+0.5y=1.3 ......(2)

Derive the value of y from equation (1)

$y=\frac{1.3-0.2x}{0.3}$ ......(3)

Substitute value of y in equation(3)

$\begin{array}{c}0.4x+0.5\left(\frac{1.3-0.2x}{0.3}\right)=2.3\\ 0.12x+0.5\left(1.3-0.2x\right)=0.69\\ 0.12x+0.65-0.1x=0.69\\ 0.02x=0.64\\ x=32\end{array}$

Substitute value of x in equation (3)

$\begin{array}{c}y=\frac{1.3-0.2\left(32\right)}{0.3}\\ =\frac{1.3-6.4}{0.3}\\ =-17\end{array}$

So, x=32 and y=-17