Question

Using the elimination method
7x-3y=18
6x+7y= 25

The answer should be (3,1)
Plz answer hurry​

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of linear equations is

$\rm :\longmapsto\:7x - 3y = 18 - - - (1)$

and

$\rm :\longmapsto\:6x + 7y = 25 - - - (2)$

On multiply equation (1) by 7 and equation (2) by 3, we get

$\rm :\longmapsto\:49x - 21y = 126 - - - (3)$

and

$\rm :\longmapsto\:18x + 21y = 75 - - - (4)$

On adding equation (3) and (4), we get

$\rm :\longmapsto\:67x = 201$

$\rm :\longmapsto\:x = \dfrac{201}{67}$

$\rm \implies\:\boxed{ \tt{ \: x \: = \: 3 \: }}$

On substituting the value of x in equation (2), we get

$\rm :\longmapsto\:6(3) + 7y = 25$

$\rm :\longmapsto\:18 + 7y = 25$

$\rm :\longmapsto\: 7y = 25 - 18$

$\rm :\longmapsto\: 7y = 7$

$\rm \implies\:\boxed{ \tt{ \: y \: = \: 1 \: }}$

Hence,

$\red{\begin{gathered}\begin{gathered}\rm :\longmapsto\:\bf\:\begin{cases} &\bf{x \: = \: 3} \\ \\ &\bf{y \: = \: 1} \end{cases}\end{gathered}\end{gathered}}$

Verification

Consider the equation

$\rm :\longmapsto\:7x - 3y = 18$

On substituting the values of x and y, we get

$\rm :\longmapsto\:7(3) - 3(1) = 18$

$\rm :\longmapsto\:21 - 3 = 18$

$\bf :\longmapsto\:18 = 18$

Hence, Verified