Question

12. Find the value of x and y 4x+7y=22, 5x-3y= 4 (Using Cross Multipfication method)​

Answer 1

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

Given pair of equations is

$\red{\rm :\longmapsto\:4x + 7y = 22}$

and

$\red{\rm :\longmapsto\:5x - 3y = 4}$

Now, using Cross multiplication method, we have

$\purple{\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf 2 & \bf 3 & \bf 1& \bf 2\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf 7 & \sf 22 & \sf 4 & \sf 7\\ \\ \sf - 3 & \sf 4 & \sf 5 & \sf - 3\\ \end{array}} \\ \end{gathered}}$

So, we have

$\green{\rm :\longmapsto\:\dfrac{x}{28 - ( - 66)} = \dfrac{y}{110 - 16} = \dfrac{ - 1}{ - 12 - 35} }$

$\green{\rm :\longmapsto\:\dfrac{x}{28 + 66} = \dfrac{y}{94} = \dfrac{ - 1}{ -47} }$

$\green{\rm :\longmapsto\:\dfrac{x}{94} = \dfrac{y}{94} = \dfrac{1}{ 47} }$

On multiply each term by 47, we get

$\green{\rm :\longmapsto\:\dfrac{x}{2} = \dfrac{y}{2} = 1}$

$\green{\bf\implies \:x = 2 \: \: \: and \: \: \: y = 2}$

Verification :-

Consider first equation,

$\red{\rm :\longmapsto\:4x + 7y = 22}$

On substituting the values of x and y, we get

$\red{\rm :\longmapsto\:4(2) + 7(2) = 22}$

$\red{\rm :\longmapsto\:8 + 14 = 22}$

$\red{\rm :\longmapsto\:22 = 22}$

Hence, Verified

Consider second equation

$\blue{\rm :\longmapsto\:5x - 3y = 4}$

On substituting the values of x and y, we get

$\blue{\rm :\longmapsto\:5(2) - 3(2) = 4}$

$\blue{\rm :\longmapsto\:10 - 6 = 4}$

$\blue{\rm :\longmapsto\:4 = 4}$

Hence, Verified