Question

$\frac{2}{ x} + \frac{2}{3y} = \frac{1}{6} \\ \frac{3}{x} + \frac{2}{y} = 0$
simultaneous equation

Answer 1

Heya..!!!

2/x + 2/3y = 1/6
3/x + 2/y = 0
∴ [ let 1/x = p , 1/y = q ]

Now,

2p + 2q/3 = 1/6

⇒6p + 2q = 1/2-----------(1)
3p + 2q = 0-----------(2)

From------(1) & -------(2)

we get,

6p + 2q = 1/2
3p + 2q = 0
(-)___(-)___(-)
------------------
3p = 1/2

⇒p = 1/6 ---put in --(2)

we get,

3(1/6) + 2q = 0

⇒1/2 + 2q = 0

⇒ 2q = - 1/2

⇒q = -1/4

⇒q = -1/4 = 1/y

⇒y = -4

AND,.

⇒p = 1/6 = 1/x

⇒x = 6

$VERIFICATION :-$

Put x = 6 , y = -4

In ----(1)

2/6 + 2/(3×-4) = 1/6

⇒1/3 - 1/6 = 1/6

⇒1/3 = 1/6 + 1/6

⇒1/3 = 2/6

⇒1/3 = 1/3

Similarly,

--------(2)

3/6 + 2/-4 = 0

⇒1/2 - 1/2 = 0

⇒0 = 0

$I HOPE ITS HELP YOU,$

Answer 2

The answer is given below :

Given,

2/x + 2/(3y) = 1/6 .....(i)

and

3/x + 2/y = 0 .....(ii)

Now, from (ii), we get

3/x = -2/y

=> 1/x = -2/(3y) .....(iii)

Putting 1/x = -2/(3y) in (i), we get

2×{-2/(3y)} + 2/(3y) = 1/6

=> -4/(3y) + 2/(3y) = 1/6

=> (-4 + 2)/(3y) = 1/6

=> -2/(3y) = 1/6

=> 3y/(-2) = 6

=> y = 6 × (-2/3)

=> y = -4

Now, from (iii), we get

1/x = -2/{3×(-4)}

=> 1/x = (-2)/(-12)

=> 1/x = 1/6

=> x = 6

Therefore, the required solution be

x = 6 and y = -4

VERIFICATION :

When x = 6 and y = -4

Left Hand Side of (i) gives

= 2/6 + 2/{3 × (-4)}

= 1/3 - 1/6

= 1/6

= Right Hand Side of (i)

and

Left Hand Side of (ii)

= 3/6 + 2/(-4)

= 1/2 - 1/2

= 0

= Right Hand Side of (ii)

Thus, verified.

Thank you for your question.