Question

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

Answer 1

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