Question

Solve using elimination method and the substitution method :

$\boxed{\sf{\dfrac{3y}{2} \:-\: \dfrac{5x}{3} \:=\: -2 \: and \: \dfrac{y}{3} \:+\: \dfrac{x}{3} \:=\: \dfrac{13}{16} }}$
ㅤㅤㅤ
• Be fast !!!!
• No spam!​

Answer 1

Answer:

x= 543/304

y= 198/304

Answer 2

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

Given pair of linear equations are

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

and

$\rm :\longmapsto\:\dfrac{y}{3} + \dfrac{x}{3} = \dfrac{13}{16} - - - - - (2)$

Solution using Elimination method :-

Equation (1) can be rewritten as

$\rm :\longmapsto\:9y - 10x = - 12 - - - (3)$

and

Equation (2) can be rewritten as

$\rm :\longmapsto\:y + x = \dfrac{39}{16} - - - (4)$

On multiply equation (4) by 9, we get

$\rm :\longmapsto\:9y + 9x = \dfrac{351}{16} - - - (5)$

On Subtracting equation (4) from equation (5), we get

$\rm :\longmapsto\:19x = \dfrac{351}{16} + 12$

$\rm :\longmapsto\:19x = \dfrac{351 + 192}{16}$

$\rm :\longmapsto\:19x = \dfrac{543}{16}$

$\bf\implies \:x = \dfrac{543}{304} - - - (6)$

On substituting the value of x, in equation (4), we get

$\rm :\longmapsto\:y + \dfrac{543}{304} = \dfrac{39}{16}$

$\rm :\longmapsto\:y = \dfrac{39}{16} - \dfrac{543}{304}$

$\rm :\longmapsto\:y = \dfrac{741 - 543}{304}$

$\bf\implies \:y = \: \dfrac{198}{304}$

Solution using Substitution method :-

From equation (4),

$\rm :\longmapsto\:y = \dfrac{39}{16} - x - - - (7)$

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

$\rm :\longmapsto\:9\bigg(\dfrac{39}{16} - x\bigg) - 10x = - 12$

$\rm :\longmapsto\:\dfrac{351}{16} - 9x - 10x = - 12$

$\rm :\longmapsto\:\dfrac{351}{16} - 19x= - 12$

$\rm :\longmapsto\:\dfrac{351}{16} + 12 = 19x$

$\rm :\longmapsto\:\dfrac{351 + 192}{16} = 19x$

$\rm :\longmapsto\:\dfrac{543}{16} = 19x$

$\bf\implies \:x = \dfrac{543}{304} - - - (8)$

On substituting the value of x, in equation (7),

$\rm :\longmapsto\:y + \dfrac{543}{304} = \dfrac{39}{16}$

$\rm :\longmapsto\:y = \dfrac{39}{16} - \dfrac{543}{304}$

$\rm :\longmapsto\:y = \dfrac{741 - 543}{304}$

$\bf\implies \:y = \: \dfrac{198}{304}$