16 / (x + y ) + 2 / (x – y)= 1; 8 / (x + y) – 12 / (x – y) = 7.

(V) 16 / (x + y ) + 2 / (x – y)= 1; 8 / (x + y) – 12 / (x – y) = 7.

Solution:

Let 1 / (x + y) = a   and  1 / ( x – y) = b

∴ the given equation will become,

16a + 2b = 1 ..... eq. no. 1

8a – 12b = 7 ..... eq. no. 2

Multiplying equation no. (2) by 2, we get

16a – 24b = 14 ... eq. no. 3

Subtracting equation no. (1) from equation no. (3)

16a – 24 b =14

16a + 2b = 1

(-)   (-)     (-)

-26b  = 13

∴ b = 13/-26

∴ b = - ½  

Substituting b = - ½ in equation no. (1)

16a + 2b = 1

∴ 16a + 2( - ½ ) = 1

∴ 16a – 1 = 1

∴ 16a = 1 + 1

∴ 16a = 2

∴ a = 2/16

∴ a = 1/8

Now, Re substituting

a = 1/(x + y)  and b = 1/( x - y)

a = 1/8 ∴ 1/ ( x + y) = 1/8 ∴ x + y = 8 ..... eq. no. 4

b =- ½ ∴ 1/(x - y ) = - ½ ∴ x – y = - 2 .... eq. no. 5

Adding equation no. (4) and equation no. (5), we get

x + y = 8

x – y = - 2

2x    = 6

∴ x = 6/2

∴ x = 3

Substituting x = 3 in equation no. 4

x + y = 8

∴  3 + y = 8

∴ y = 8 – 3

∴ y = 5

Ans. x = 3 and y = 5.