Question

Solve the pair of linear equations 9x -4y+1=0, 7x –6y-5=0using crossmultiplication method.

Answer 1

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

Given pair of linear equations are

$\rm :\longmapsto\:9x - 4y + 1 = 0$

and

$\rm :\longmapsto\:7x - 6y - 5 = 0$

can be rewritten as

$\rm :\longmapsto\:9x - 4y = - 1$

and

$\rm :\longmapsto\:7x - 6y = 5$

Using Cross Multiplication method, we have

$\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf 2 & \bf 3 & \bf 1& \bf 2\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf - 4 & \sf - 1 & \sf 9 & \sf - 4\\ \\ \sf - 6 & \sf 5 & \sf 7 & \sf - 6\\ \end{array}} \\ \end{gathered}$

So,

$\rm :\longmapsto\:\dfrac{x}{ - 20 - 6} = \dfrac{y}{ - 7 - 45} = \dfrac{ - 1}{ - 54 - ( - 28)}$

$\rm :\longmapsto\:\dfrac{x}{ - 26} = \dfrac{y}{ - 52} = \dfrac{ - 1}{ - 54 + 28}$

$\rm :\longmapsto\:\dfrac{x}{ - 26} = \dfrac{y}{ - 52} = \dfrac{ - 1}{ - 26}$

$\rm :\longmapsto\:\dfrac{x}{ - 26} = \dfrac{y}{ - 52} = \dfrac{ 1}{ 26}$

On taking first and third member, we get

$\rm :\longmapsto\:\dfrac{x}{ - 26} = \dfrac{ 1}{ 26}$

$\bf\implies \:x = - 1$

Now,

On taking second and third member, we get

$\rm :\longmapsto\: \dfrac{y}{ - 52} = \dfrac{ 1}{ 26}$

$\rm :\longmapsto\:y = - \dfrac{52}{26}$

$\bf\implies \:y = - \: 2$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Solution \: is \: \begin{cases} &\bf{x \: = \: - \: 1} \\ &\bf{y \: = \: - \: 2} \end{cases}\end{gathered}\end{gathered}$

Verification :-

Consider Equation (1),

$\rm :\longmapsto\:9x - 4y + 1 = 0$

On substituting the values of x and y, we get

$\rm :\longmapsto\:9( - 1) - 4( - 2) + 1 = 0$

$\rm :\longmapsto\: - 9 + 8 + 1 = 0$

$\rm :\longmapsto\:0 = 0$

Hence, Verified

Consider Equation (2),

$\rm :\longmapsto\:7x - 6y - 5 = 0$

On substituting the values of x and y, we get

$\rm :\longmapsto\:7( - 1) - 6( - 2) - 5 = 0$

$\rm :\longmapsto\: - 7 + 12 - 5 = 0$

$\rm :\longmapsto\:12 - 12 = 0$

$\rm :\longmapsto\:0 = 0$

Hence, Verified

Answer 2

this

is

correct

answer

.