Question

Solve 2xy/x+y=3/2,2xy/2x-y=-3/10,x+y not= 0,2x-y not =
0

Answer 1

In the attachment I have answered this problem.

The given equations are suitably modified and are solved by elimination method.

See the attachment for detailed solution.

Answer 2

Given Equations,

2xy/(x + y) = 3/2
⇒ 2xy × 2 = 3(x + y)
⇒ 4xy = 3x + 3y
⇒ 3y + 3x = 4xy 
∴ x = (4xy - 3y)/3 --------------------eq(i)

Now,
2xy/(2x - y) = -3/10
⇒ 2xy × 10 = -3(2x- y)
⇒ 20xy = -6x + 3y
⇒ 3y - 6x = 20xy ----------------------eq(ii)

Using the Substitution method for finding the value of x and y.

Putting the Value of eq(i) into the eq(ii),
3y - 6x = 20xy
⇒ 3y - 6(4xy - 3y)/3 = 20xy
∴ 3y - 8xy + 6y = 20xy
∴ 9y - 8xy = 20xy
∴ 9y = 28xy
∴ 28x = 9
∴ x = 9/28

Now, Putting the Value of the x in eq(ii), ∴ 3y - 6x = 20xy

∴ 3y = 20xy + 6x
∴ 3y = 20y(9/28) + 6(9/28)
  45y/7 - 3y = -27/14
⇒ (45y - 21y)/7 = -27/14
⇒ 24y = -27/2
⇒ y = -9/16


Hence, the value of x is 9/28 and the value of y is -9/16.


Hope it helps.