xy÷x+y=6÷5 ,xy ÷y-x=6
Answers
Answer:
x = 2 , y = 3
Solution:
The given equations are :
xy/(x + y) = 6/5 -------(1)
xy/(x - y) = 6 -------(2)
Eq-(1) can be rewritten as ;
=> xy/(x + y) = 6/5
{ Reciprocal both the sides }
=> (x + y)/xy = 5/6
{ separate division }
=> x/xy + y/xy = 5/6
=> 1/y + 1/x = 5/6
=> 1/x + 1/y = 5/6 ---------(3)
Eq-(2) can be rewritten as ;
=> xy/(y - x) = 6
{ Reciprocal both the sides }
=> (y - x)/xy = 1/6
{ separate division }
=> y/xy - x/xy = 1/6
=> 1/x - 1/y = 1/6 ---------(4)
Now,
Adding eq-(3) and eq-(4) ,
We get ;
=> 1/x + 1/y + 1/x - 1/y = 5/6 + 1/6
=> 1/x + 1/x = (5+1)/6
=> 2/x = 6/6
=> 2/x = 1
=> x/2 = 1
=> x = 2
Now,
Putting x = 2 in eq-(3) , we get ;
=> 1/x + 1/y = 5/6
=> 1/2 + 1/y = 5/6
=> 1/y = 5/6 - 1/2
=> 1/y = (5 - 3)/6
=> 1/y = 2/6
=> 1/y = 1/3
=> y = 3
Hence,
x = 2 and y = 3