Question

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

$x+y=5$

$2x-3y=4$

Answer 1

Given :

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

Multiply equation $\left(1\right)$ by $3$, we get,

$3x+3y=15.....\left(3\right)$

Now adding equation $\left(2\right)$ and equation $\left(3\right)$, we get,

$$\begin{gathered} 2x-3y+3x+3y=4+15 \\ \Rightarrow 5x=19 \\ \Rightarrow x=\frac{19}{5} \end{gathered}$$

Now, putting the value of $x$ in equation $\left(1\right)$, we get

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

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 for the given equation.