27/(x-2 )+31/(y+3 )=85; 31/(x-2)+27/(y+3)=89.

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 

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