Question

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

$$\begin{gathered} x+y=14 \\ x-y=4 \end{gathered}$$

Answer 1

$$\begin{gathered} x+y=14......\left(1\right) \\ x-y=4......\left(2\right) \end{gathered}$$

From $1^{st}$ equation, we get,

$x=14–y......\left(3\right)$

Now, substitute the value of $x$ in $2^{nd}$ equation to get,

$$\begin{gathered} (14–y)–y=4 \\ \Rightarrow 14–2y=4 \\ \Rightarrow 2y=10 \\ \Rightarrow y=5 \end{gathered}$$

By the value of $y$, we can now find the exact value of $x$;

$$\begin{gathered} \because x=14–y \\ \Rightarrow x=14-5 \\ \Rightarrow x=9 \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{9}$ and $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{5}$ are the solution of given pair of equation.