(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.