Question

use method of cross multiplication to solve x +2y=3 and 2x + 9y=5

Answer 1

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

Given pair of linear equations are

$\rm :\longmapsto\:x + 2y = 3$

and

$\rm :\longmapsto\:2x + 9y = 5$

Now, using Cross Multiplication method, we have

$\red{\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf 2 & \bf 3 & \bf 1& \bf 2\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf 2 & \sf 3 & \sf 1 & \sf 2\\ \\ \sf 9 & \sf 5 & \sf 2 & \sf 9\\ \end{array}} \\ \end{gathered}}$

So, we get

$\rm :\longmapsto\:\dfrac{x}{10 - 27} = \dfrac{y}{6 - 5} = \dfrac{ - 1}{9 - 4}$

$\rm :\longmapsto\:\dfrac{x}{-17} = \dfrac{y}{1} = \dfrac{ - 1}{5}$

$\rm :\longmapsto\:\dfrac{x}{-17} = \dfrac{y}{1} = \dfrac{- 1}{5}$

Taking first and third member, we get

x = 17/5

Taking second and third member, we get

y = - 1/5

Verification :-

Consider first equation, we get

x + 2y = 3

On substituting the values of x and y, we get

17/5 - 2/5 = 3

15/5 = 3

3 = 3

Hence, Verified