Question

Cross multiplication 2x+y=35 3x+4y=65

Answer 1

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

Given pair of linear equations are

$\rm :\longmapsto\:2x + y = 35$

and

$\rm :\longmapsto\:3x + 4y = 65$

Now, by using Cross Multiplication method, we have

$\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf 2 & \bf 3 & \bf 1& \bf 2\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf 1 & \sf 35 & \sf 2 & \sf 1\\ \\ \sf 4 & \sf 65 & \sf 3 & \sf 4\\ \end{array}} \\ \end{gathered}$

Now,

$\rm :\longmapsto\:\dfrac{x}{65 - 140} = \dfrac{y}{105 - 130} = \dfrac{ - 1}{8 - 3}$

$\rm :\longmapsto\:\dfrac{x}{ - 75} = \dfrac{y}{ - 25} = \dfrac{ - 1}{5}$

$\rm :\longmapsto\:\dfrac{x}{ - 75} = \dfrac{y}{ - 25} = \dfrac{1}{ - 5}$

On multiply each term by - 5,

$\rm :\longmapsto\:\dfrac{x}{15} = \dfrac{y}{5} =1$

$\bf\implies \:x = 15$

and

$\bf\implies \:y = 5$

Check the solution :-

Let us consider equation (1),

$\rm :\longmapsto\:2x + y = 35$

On substitute the values of x = 15 and y = 5,

$\rm :\longmapsto\:2 \times 15 + 5 = 35$

$\rm :\longmapsto\:30 + 5 = 35$

$\rm :\longmapsto\:35= 35$

Hence, verified