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.


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