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.

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