Question

2/x + 2/3y=1/6 ;3/x + 2/y=0

Answer 1

x=16 and y=3 this is the answer

Answer 2

Question :-

Solve for x and y :-

$\rm \frac{2}{x} + \frac{2}{3y} = \frac{1}{6}$

$\rm \frac{3}{x} + \frac{2}{y} = 0$

Answer :-

Let,

$\rm \frac{1}{x} = u$

$\rm \frac{1}{y} = v$

Substituting in equation -

➩ $\rm 2u + \frac{2}{3}v = \frac{1}{6}$ - ➀

➩ $\rm 3u + 2y = 0$- ➁

Multiplying the equation ➀ by 3

and equation ➁ by 2

Equation ➀ -

➩ $\rm 3 ( 2u + \frac{2}{3}v = \frac{1}{6} )$

➩ $\rm 6u + 2v = \frac{1}{2}$- ➂

Equation ➁ -

➩ $\rm 2 ( 3u + 2y ) = 0$

➩ $\rm 6u + 4v = 0$ - ➃

Subtracting the equation ➂ from ➃

➩ $\rm 6u + 4v - 6u - 2v = 0 - \frac{1}{2}$

➩ $\rm 2v = - \frac{1}{2}$

$\rm v = - \frac{1}{4}$

Substituting the value of v in equation ➀

➩ $\rm 2u + \frac{2}{3}v = \frac{1}{6}$

➩ $\rm 2u + \frac{2}{3} \times \frac{-1}{4}= \frac{1}{6}$

➩ $\rm 2u + \frac{-1}{6}v = \frac{1}{6}$

➩ $\rm 2u = \frac{1}{6} + \frac{1}{6}$

$\rm u = \frac{1}{6}$

$\rm x = \frac{1}{u}$

➱$\boxed{\rm x = 6 }$

$\rm y = \frac{1}{v}$

➱ $\boxed{\rm y = -4 }$