Question

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

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

Answer 1

Given :

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

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

$x=5–y\dots \dots ..\left(3\right)$

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

$$\begin{gathered} 2(5–y)–3y=4 \\ \Rightarrow 10-2y-3y=4 \\ \Rightarrow -5y=4-10 \\ \Rightarrow -5y=-6 \\ \Rightarrow y=\frac{6}{5} \end{gathered}$$

When the value of $y$ is substituted in equation $\left(3\right)$, we obtain:

$$\begin{gathered} x=5-\frac{6}{5} \\ \Rightarrow x=\frac{25-6}{5} \\ \Rightarrow x=\frac{19}{5} \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{19}}{\mathbf{5}}$ and $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{6}}{\mathbf{5}}$ are the solutions of given equations.