Question

can any please solve this question

Answer 1

Answer :

x = 2 , y = 5

Solution :

Here ,

The given equations are ;

4/x - 5/y = (x + y)/xy + 3/10 -------(1)

3xy = 10(y - x) ---------(2)

Eq-(1) can be rewritten as ;

=> 4/x - 5/y = (x + y)/xy + 3/10

=> 4/x - 5/y = x/xy + y/xy + 3/10

=> 4/x - 5/y = 1/y + 1/x + 3/10

=> 4/x - 1/x - 5/y - 1/y = 3/10

=> 3/x - 6/y = 3/10

=> 3(1/x - 2/y) = 3/10

=> 1/x - 2/y = 1/10

=> 10(1/x - 2/y) = 1

=> 10/x - 20/y = 1

=> 10/x = 1 + 20/y -------(3)

Eq-(2) can be rewritten as ;

=> 3xy = 10(y - x)

=> 3 = 10(y - x)/xy

=> 3 = 10(y/xy - x/xy)

=> 3 = 10(1/x - 1/y)

=> 3 = 10/x - 10/y

=> 10/x = 3 + 10/y ------(4)

From eq-(3) and (4) , we have ;

=> 1 + 20/y = 3 + 10/y

=> 20/y - 10/y = 3 - 1

=> 10/y = 2

=> 10/2 = y

=> 5 = y

=> y = 5

Now ,

Putting y = 5 in eq-(3) , we get ;

=> 10/x = 1 + 20/y

=> 10/x = 1 + 20/5

=> 10/x = 1 + 4

=> 10/x = 5

=> 10/5 = x

=> 2 = x

=> x = 2

Hence ,

x = 2 , y = 5