1/3x + 1/5y = 1/15; 1/2x + 1/3y = 1/12

(iii) 1/3x + 1/5y = 1/15;  1/2x + 1/3y = 1/12

1/3x + 1/5y = 1/15

Multiplying the equation by 15 on both the sides we get,

5/x + 3/y = 1

1/2x + 1/3y = 1/12

Multiplying the equation by 12 on both the sides we get,

6/x + 4/y = 1

Now,

Let 1/x = a and 1/y = b

∴ We get, 5a + 3b = 1 ......... eq. no. (1)

and 6a + 4b = 1 ........ eq. no. (2)

Multiplying (1) bt 4, we get

20a + 12b = 4 .........(3)

Multiplying (2) by 3, we get

18a + 12b = 3 ........(vi)

Subtracting  (4) from (3),

20a	+12b	=	4
18a	+12b	=	3
(-)	(-)		(-)
2a		=	1

∴ a = 1/2

Substituting a = 1/2  in equation (2)

∴ 6a + 4b = 1

∴ 6(1/2) + 4b = 1

∴ 3 + 4b = 1

∴ 4b = 1 – 3

∴ 4b = - 2

∴ b= - 2 /4

∴ b = -1/2

Substituting the values of a and b,

a = 1/2 ∴ 1/x = 1/2 ∴ x = 2

b = -1/2 ∴ 1/y = -1/2 ∴ y = -2

∴ x = 2  and y = - 2 is the solution of given simultaneous equations.