Question

answer me
maths
ch. simultaneous linear equations
solve it by substitution method​

Answer 1

Given Question :-

Solve the following equations by Method of Substitution

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

and

$\rm :\longmapsto\:9x - 2y = 7$

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

Given lines are

$\rm :\longmapsto\:3x - 5y = 4 - - - (1)$

and

$\rm :\longmapsto\:9x - 2y = 7$

$\rm :\longmapsto\:9x = 7 + 2y$

$\bf\implies \:\boxed{ \tt{ \: \: x = \dfrac{7 + 2y}{9} \: \: }} - - - (2)$

On substituting the value of x from equation (2), in equation (1), we get

$\rm :\longmapsto\:3\bigg[\dfrac{7 + 2y}{9} \bigg] - 5y = 4$

$\rm :\longmapsto\:\bigg[\dfrac{7 + 2y}{3} \bigg] - 5y = 4$

$\rm :\longmapsto\:\dfrac{7 + 2y - 15y}{3} = 4$

$\rm :\longmapsto\:\dfrac{7 - 13y}{3} = 4$

$\rm :\longmapsto\:7 - 13y = 12$

$\rm :\longmapsto\:- 13y = 12 - 7$

$\rm :\longmapsto\:- 13y = 5$

$\bf\implies \:\boxed{ \tt{ \: y = - \: \frac{5}{13} \: \: }}$

Now, on substituting the value of y, in equation (2), we get

$\rm :\longmapsto\:x = \dfrac{1}{9}\bigg[7 + 2 \times \dfrac{ (- 5)}{13} \bigg]$

$\rm :\longmapsto\:x = \dfrac{1}{9}\bigg[7 - \dfrac{10}{13} \bigg]$

$\rm :\longmapsto\:x = \dfrac{1}{9}\bigg[\dfrac{91 - 10}{13} \bigg]$

$\rm :\longmapsto\:x = \dfrac{1}{9}\bigg[\dfrac{81}{13} \bigg]$

$\bf\implies \:\boxed{ \tt{ \: x= \: \frac{9}{13} \: \: }}$

Answer 2

Answer:

Step-by-step explanation: