Question

(i) 4x – 5y + 7 = 0
3х – 4у +6 = 0
Solve by Cross Multiplication method​

Answer 1

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

Given pair of linear equations are

$\rm :\longmapsto\:4x - 5y + 7 = 0$

and

$\rm :\longmapsto\:3x - 4y + 6 = 0$

which can be rewrite as

$\rm :\longmapsto\:4x - 5y = - \: 7$

and

$\rm :\longmapsto\:3x - 4y = - \: 6$

Now, by using Cross Multiplication method, we get

$\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf 2 & \bf 3 & \bf 1& \bf 2\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf - 5 & \sf - 7 & \sf 4 & \sf - 5\\ \\ \sf - 4 & \sf - 6 & \sf 3 & \sf - 4\\ \end{array}} \\ \end{gathered}$

Now,

$\rm :\longmapsto\:\dfrac{x}{30 - 28} = \dfrac{y}{ - 21 + 24} = \dfrac{ - 1}{ - 16 + 15}$

$\rm :\longmapsto\:\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{ - 1}{ - 1}$

$\rm :\longmapsto\:\dfrac{x}{2} = \dfrac{y}{3} = 1$

$\bf\implies \:x = 2$

and

$\bf\implies \:y = 3$

Check the Solution :

Consider equation (1),

$\rm :\longmapsto\:4x - 5y = - \: 7$

On substitute the value of x = 2 and y = 3,

$\rm :\longmapsto\:4 \times 2 - 5 \times 3 = - \: 7$

$\rm :\longmapsto\: 8 - 15 = - 7$

$\rm :\longmapsto\: - 7 = - 7$

Hence, verified.