Question

3x/2-5y/3=-2 this is equation no 1 and x/3+y/2 =13/6 this is equation no 2

Answer 1

In equation 1,

$\implies \dfrac{3x}{2} - \dfrac{5y}{3} = - 2\\\\\\\implies \dfrac{ 9x -10y }{6} = - 2 \\\\\\\implies 9x-10y = - 12$

9x - 10y = - 12          ...( i )

In equation 2,

$\implies \dfrac{x}{3} + \dfrac{y}{2} = \dfrac{13}{6} \\\\\\\implies \dfrac{2x+3y}{6} = \dfrac{13}{6}\\\\\\\implies 2x+3y= \dfrac{13\times 6}{6}\\\\\\\implies 2x+3y=13$

2x + 3y = 13           ....( ii )

Now, equations are 9x - 10y = - 12 and 2x + 3y = 13.

Multiply by 2 on both sides of ( i ),

⇒ 2( 9x - 10y ) = 2( - 12 )

⇒ 18x - 20y = - 24

Multiply by 9 on both sides of ( ii ),

⇒ 9( 2x + 3y ) = 9( 13 )

⇒ 18x + 27y = 117

Subtract [ 18x + 27y = 117 ] from [ 18x - 20y = - 24 ],

18x - 20y = - 24

18x + 27y = 117

-     -            -

_______________

      47y  = 141

_______________

y = $\dfrac{141}{47}$

y = 3

Substitute the value of y in ( i ),

⇒ 9x - 10y = - 12

⇒ 9x -10( 3 ) = - 12

⇒ 9x - 30 = - 12

⇒ 9x = - 12 + 30

⇒ 9x = 18

⇒ x = 18 / 9

⇒ x = 2

Therefore the value of x is 2 and value of y is 3.