Question

find the value of x and y if x+y=2xy and x-y=6xy

Answer 1

x+y=2xy.............(1)

x-y=6xy........(2)

Divide eq(1) & (2) by XY on both sides

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

1/y +1/x = 2...............(3)

x/xy - y/xy = 6xy/xy

1/y - 1/x = 6....................(4)

Adding eq (3) & (4)

1/y +1/y = 6+2

2/y = 8

8y = 2

y= 2/8 = 1/4

y= 1/4

Put this value of y in eq (3)

1/y +1/x = 2

4+ 1/x = 2

1/x = 2-4

1/x =-2

x= -1/2

Hence, the value of x = -1/2 & y = 1/4

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Hope this will help you...

Answer 2

x + y = 2 xy  ................. (1)
x - y = 6 xy   ................. (2)
We have to find the values of x and y.
First of all, add both the equations, we get:
(x + y) + (x - y) = 2xy + 6xy
2x = 8 xy
Simplifying x on both sides, we get:
2 = 8 y
On further simplification, we get:
1 = 4 y
y = 1/4
which is the required value of y.
For calculating the value of x, put the value of y in any of the above two equations.
We put the value of y in equation (1)
x + y = 2 xy
x + 1/4 = 2 (x) (1/4)
x + 1/4 = x/2
x - x/2 = - 1/4
Taking x common, we get:
x (1 - 1/2) = -1/4
x (1/2) = - 1/4
x = (-1/4) (2)
x = - 1/2
which is the required value of x.
The value of x can also be calculated by putting the value of y in equation (2).