Question

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

$$\begin{gathered} 0.2x+0.3y=1.3 \\ 0.4x+0.5y=2.3 \end{gathered}$$

Answer 1

Solve the linear equations:

$$\begin{gathered} 0.2x+0.3y=1.3........\left(1\right) \\ 0.4x+0.5y=2.3........\left(2\right) \end{gathered}$$

From equation $\left(1\right)$, we obtain

$$\begin{gathered} 0.2x=1.3-0.3y \\ \Rightarrow x=\frac{1.3-0.3y}{0.2}......\left(3\right) \end{gathered}$$

Substituting the value of $x$ in equation $\left(2\right)$, we obtain

$$\begin{gathered} 0.4\left(\frac{1.3-0.3y}{0.2}\right)+0.5y=2.3 \\ \Rightarrow 2(1.3-0.3y)+0.5y=2.3 \\ \Rightarrow 2.6-0.6y+0.5y=2.3 \\ \Rightarrow -0.1y=2.3-2.6 \\ \Rightarrow -0.1y=-0.3 \\ \Rightarrow y=\frac{-0.3}{-0.1} \\ \Rightarrow y=3 \end{gathered}$$

Now, substituting the value of $y$ in equation $\left(3\right)$, we obtain

$$\begin{gathered} x=\frac{1.3-0.3\left(3\right)}{0.2} \\ \Rightarrow x=\frac{1.3-0.9}{0.2} \\ \Rightarrow x=\frac{0.4}{0.2} \\ \Rightarrow x=2 \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2}$ and $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}$ are the solution of given pair of equation.