Question

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

$$\begin{gathered} 8x+5y=9 \\ 3x+2y=4 \end{gathered}$$

Answer 1

$$\begin{gathered} 8x+5y=9......\left(1\right) \\ 3x+2y=4......\left(2\right) \end{gathered}$$

Taking equation $\left(1\right)$, we have:

$$\begin{gathered} 8x+5y=9 \\ \Rightarrow 5y=9-8x \\ \Rightarrow y=\frac{9-8x}{5}......\left(3\right) \end{gathered}$$

On substituting the value of $y$ in equation $\left(2\right)$, we have

$$\begin{gathered} 3x+2\left(\frac{9-8x}{5}\right)=4 \\ \Rightarrow 3x+\frac{18-16x}{5}=4 \\ \Rightarrow \frac{15x+18-16x}{5}=4 \\ \Rightarrow 18-x=20 \\ \Rightarrow -x=20-18 \\ \Rightarrow x=-2 \end{gathered}$$

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

$$\begin{gathered} y=\frac{9-8(-2)}{5} \\ \Rightarrow y=\frac{9+16}{5} \\ \Rightarrow y=\frac{25}{5} \\ \Rightarrow y=5 \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{2}$ and $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{5}$ is the solution of given equation.