2/x + 6/y = 13; 3/x + 4/y = 12

(ii) 2/x + 6/y = 13; 3/x + 4/y = 12

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

∴ We get, 2a + 6b = 13 ......... eq. no. (1)

and 3a + 4b = 12 ........ eq. no. (2)

Multiplying (1) by 2,

4a + 12b= 26 .......(3)

Multiplying (2) by 3,

9a + 12b= 36 ......(4)

Subtracting  (3) from (4),

9a	+12b	=	36
4a	+12b	=	26
(-)	(-)		(-)
5a		=	10

∴ a = 10/5

∴ a = 2

Substituting a = 2 in (1),

2 (2) + 6b = 13

∴  4 + 6b = 13

∴  6b = 13 – 4

∴ b = 9/6

∴ b = 3/2

Substituting the values of a and b,

a = 2 ∴ 1/x = 2 ∴ x = 1/2

b = 3/2 ∴ 1/y = 3/2 ∴ y = 2/3

∴ x = 1/2  and y = 2/3 is the solution of given simultaneous equations.