Question

please solve this by substitution method​

Answer 1

$\large\underline{\sf{Given \:Question - }}$

Solve the given system of equations by Substitution method :

$\rm :\longmapsto\:\dfrac{3}{5}x - \dfrac{2}{3}y = - 1$

$\rm :\longmapsto\:\dfrac{1}{10}x + \dfrac{4}{9}y = \dfrac{9}{2}$

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

Given pair of linear equations are

$\rm :\longmapsto\:\dfrac{3}{5}x - \dfrac{2}{3}y = - 1 - - - (1)$

and

$\rm :\longmapsto\:\dfrac{1}{10}x + \dfrac{4}{9}y = \dfrac{9}{2} - - - (2)$

Now, Consider equation (1),

$\rm :\longmapsto\:\dfrac{3}{5}x - \dfrac{2}{3}y = - 1$

$\rm :\longmapsto\:\dfrac{3x}{5} = \dfrac{2y}{3} - 1$

$\rm :\longmapsto\:\dfrac{3x}{5} = \dfrac{2y - 3}{3}$

$\rm :\longmapsto\:x = \dfrac{10y - 15}{9} - - - - (3)$

On substituting the value of x in equation (2),

$\rm :\longmapsto\:\dfrac{x}{10} + \dfrac{4y}{9} = \dfrac{9}{2}$

$\rm :\longmapsto\:\dfrac{10y - 15}{90} + \dfrac{4y}{9} = \dfrac{9}{2}$

$\rm :\longmapsto\:\dfrac{10y - 15 + 40y}{90} = \dfrac{9}{2}$

$\rm :\longmapsto\:\dfrac{50y - 15 }{90} = \dfrac{9}{2}$

$\rm :\longmapsto\:\dfrac{5(10y - 3) }{90} = \dfrac{9}{2}$

$\rm :\longmapsto\:\dfrac{(10y - 3) }{18} = \dfrac{9}{2}$

$\rm :\longmapsto\:10y - 3 = 81$

$\rm :\longmapsto\:10y = 81 + 3$

$\rm :\longmapsto\:10y = 84$

$\bf\implies \:y = \dfrac{42}{5} - - - - (4)$

On substituting the value of y in equation (3), we get

$\rm :\longmapsto\:x = \dfrac{10 \times \dfrac{42}{5} - 15}{9}$

$\rm :\longmapsto\:x = \dfrac{\dfrac{420}{5} - 15}{9}$

$\rm :\longmapsto\:x = \dfrac{\dfrac{420 - 75}{5}}{9}$

$\rm :\longmapsto\:x = \dfrac{\dfrac{345}{5}}{9}$

$\rm :\longmapsto\:x = \dfrac{69}{9}$

$\rm :\longmapsto\:x = \dfrac{23}{3}$

Justification :-

Consider equation (2),

$\rm :\longmapsto\:\dfrac{1}{10}x + \dfrac{4}{9}y = \dfrac{9}{2}$

On substituting the values of x and y, we get

$\rm :\longmapsto\:\dfrac{1}{10} \times \dfrac{23}{3} + \dfrac{4}{9} \times \dfrac{42}{5} = \dfrac{9}{2}$

$\rm :\longmapsto\: \dfrac{23}{30} + \dfrac{56}{15} = \dfrac{9}{2}$

$\rm :\longmapsto\: \dfrac{23 + 112}{30} = \dfrac{9}{2}$

$\rm :\longmapsto\: \dfrac{135}{30} = \dfrac{9}{2}$

$\rm :\longmapsto\: \dfrac{9}{2} = \dfrac{9}{2}$

Hence, Verified

Answer 2

$\color{orange}hope \: i t \: help \: you\:✌✌☺❤ \\ \\ \small\red{\boxed{\boxed{it's᭄亗 乄 ＭꫝղᎥនh 乄 亗✯❤࿐}}}$