Q. 4 B3.7( 10 Votes )

Attempt any two s

Answer :

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

Let 1/(x-2) = a and 1/(y+3) = b


Given equations becomes


27a + 31b = 85 ………………..(1)


31a + 27b = 89 ………………..(2)


Adding (1) and (2)


27a + 31b + 31a + 27b = 85 + 89


58a + 58b = 174


58 (a + b) = 174


a + b = 3 …………………(3)


Subtracting equation (1) and (2)


27a + 31b – 31a – 27b = 89


-4a + 4b = -4


a – b = 1 …………………(4)


Adding equation (3) and (4)


a + b + a – b = 4


2a = 4


a = 4/2


a = 2


Putting value of a in (4)


2 – b = 1


b = 2 – 1


b = 1


Resubstituting


a = 1/(x – 2)


1/(x – 2) = 2


1 = 2x – 4


2x = 1 + 4


x = 5/2


b = 1/(y + 3)


1 = 1/(y + 3)


y + 3 = 1


y = 1 – 3


y = -2


x = 5/2 and y = -2


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