Question

1/x+y+1/x-y=7;1/x+y-1/x-y=1

Answer 1

Answer :

x = 7/24 , y = -1/24

Solution :

Here ,

The given equations are ;

1/(x + y) + 1/(x - y) = 7 --------(1)

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

Adding eq-(1) and (2) , we have ;

=> 1/(x + y) + 1/(x - y) + 1/(x + y) - 1/(x - y) = 7 + 1

=> 2/(x + y) = 8

=> x + y = 2/8

=> x + y = 1/4 ----------(3)

Now ,

Putting x + y = 1/4 in eq-(1) , we have ;

=> 1/(x + y) + 1/(x - y) = 7

=> 1/¼ + 1/(x - y) = 7

=> 4 + 1/(x - y) = 7

=> 1/(x - y) = 7 - 4

=> 1/(x - y) = 3

=> x - y = 1/3 ---------(4)

Now ,

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

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

=> 2x = (3 + 4)/(4•3)

=> 2x = 7/12

=> x = 7/(12•2)

=> x = 7/24

Now ,

Putting x = 7/24 in eq-(3) , we have ;

=> x + y = 1/4

=> y = 1/4 - x

=> y = 1/4 - 7/24

=> y = (6 - 7)/24

=> y = -1/24

Hence ; x = 7/24 , y = -1/24