iv. 27/(x-2 )+31/(y+3 )=85; 31/(x-2)+27/(y+3)=89.
Solution:
Let 1/(x-2)=a and 1/(y+3)=b
∴ the given equations become
27a+31b=85
.................... eq. no. 1
31a+27b=89
.................... eq. no. 2
Adding equation (1) and
(2)
27a+13
b=85
|
31a+27
b=89
|
58a+58b=174
|
∴
58(a+b)= 174
∴
a+b=174/58
∴
a+b=3 ................. eq. no. 3
Now, subtracting
equation (1) and (2)
27a+13
b=85
|
31a+27
b=89
|
(-) (-)
(-)
|
-4a
+ 4b = -4
|
∴
- 4 (a – b) = - 4
∴
a – b = -4/-4
∴
a – b = 1 .......... eq. no. 4
Adding equation (3) and
(4)
a
+ b = 3
|
a
– b = 1
|
2a = 4
|
∴ a
= 4/2
∴
a = 2
Substituting a = 2 in equation (3)
a
+ b = 3
∴
2 + b = 3
∴
b = 3 – 2
∴
b = 1
Now, Re substituting
a
=
1/(x – 2) and b = 1/(
y + 3)
a
= 2
∴
1/(x – 2) = 2
∴
1 = 2x – 4
∴
1 + 4 = 2x
∴
5 = 2x
∴
x = 5/2
|
b
= 1
∴
1/(y + 3 ) = 1
∴
1 = y + 3
∴
1 – 3 = y
∴
y = - 2
|
Ans. x = 5/2 and y = - 2