Question

$x+7y=10,3x-2y=7;$solve the following.

Answer 1

Solution of pair of linear equation:

Consider,

$$\begin{gathered} x+7y=10...\left(1\right) \\ 3x-2y=7...\left(2\right) \end{gathered}$$

Multiply equation $\left(1\right)$ by $3$ and subtract equation $\left(2\right)$ from it.

$$\begin{gathered} 3x+21y-\left(3x-2y\right)=30-7 \\ \Rightarrow 3x+21y-3x+2y=30-7 \\ \Rightarrow 23y=23 \\ \Rightarrow y=\frac{23}{23} \\ \therefore y=1 \end{gathered}$$

Put $y=1$in equation $\left(1\right)$

$$\begin{gathered} x+7\times 1=10 \\ \Rightarrow x+7=10 \\ \Rightarrow x=10-7 \\ \therefore x=3 \end{gathered}$$

Hence, the solution is $\mathit{x}\mathbf{=}\mathbf{3}$ and $\mathit{y}\mathbf{=}\mathbf{1}$.