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. 

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