Question

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Answer 1

Answer :

x = 14/5 , y = 23/12

Solution :

The given equation are ;

5/(x - 1) + 1/(y - 2) = 2 --------(1)

6/(x - 1) + 3/(y - 2) = 1 ----------(2)

Substituting 1/(x - 1) = a and 1/(y - 2) = b , equations (1) and (2) will reduce to linear equations as follow ;

5a + b = 2 ---------(3)

6a + 3b = 1 ---------(4)

Using eq-(3) , we have ;

=> 5a + b = 2

=> b = 2 - 5a --------(5)

Putting b = 2 - 5a in eq-(4) , we have ;

=> 6a + 3a = 1

=> 6a + 3(2 - 5a) = 1

=> 6a + 6 - 15a = 1

=> 6a - 15a = 1 - 6

=> -9a = -5

=> a = -5/-9

=> a = 5/9

=> 1/(x - 1) = 5/9

=> x - 1 = 9/5

=> x = 9/5 + 1

=> x = (9+5)/5

=> x = 14/5

Now ,

Putting a = 5/9 in eq-(5) , we get ;

=> b = 2 - 5a

=> b = 2 - 5•(14/5)

=> b = 2 - 14

=> b = -12

=> 1/(y - 2) = -12

=> y - 2 = -1/12

=> y = 2 - 1/12

=> y = (24 - 1)/12

=> y = 23/12

Hence ,

x = 14/5 , y = 23/12