Question

Solve the following systems of equations :
x + y = 2xy
(x – y)/xy = 6 where x ≠ 0, y ≠ 0

Answer 1

Answer:

x = - 1/2 , y = 1/4

Step-by-step explanation:

Given----> x + y = 2xy

( x - y ) / xy = 6

To find ------> Value of x and y .

Solution------> ATQ,

x + y = 2xy

Dividing by xy , we get,

=> x / xy + y / xy = 2xy / xy

=> 1 / y + 1 / x = 2 ...................( 1 )

( x - y ) / xy = 6

=> x / xy - y / xy = 6

=> 1 / y - 1 / x = 6 ..................( 2 )

Adding equation ( 1 ) and ( 2 ) .

1 / y + 1 / x + 1 / y - 1 / x = 2 + 6

=> 2 / y = 8

=> 8y = 2

=> y = 2 / 8

=> y = 1 / 4

Putting y = 1 / 4 in equation ( 1 )

1 / y + 1 / x = 2

=> 1 / ( 1/4 ) +1 / x = 2

=> 4 + 1 / x = 2

=> 1 / x = 2 - 4

=> 1 / x = - 2

=> x = - 1 / 2