Question

Solve : 
`[2xy]/[ x + y ] = 3/2`

`[xy]/[ 2x - y ] = -3/10`
x + y ≠ 0 and 2x - y ≠ 0 

Answer 1

`[2xy]/[ x + y ] = 3/2`

⇒ `[ x + y ]/[ xy ] = 4/3`

⇒ `1/x + 1/y = 4/3`              .....(1)

`[xy]/[ 2x - y ] = -3/10`

⇒ `[ 2x - y ]/[ xy ] = - 10/3`

⇒ `-1/x + 2/y = - 10/3`        ......(2)

Let `1/x = u and 1/y = v`
Then, equations (1) and (2) become
u + v = `4/3   and  - u + 2v = - 10/3`

⇒ 3u + 3v = 4 and -3u + 6v = -10
Adding, We have
9v = - 6
⇒ v = `-6/9 = - 2/3`

⇒ `1/y = - 2/3 `
⇒ y = `-3/2`

Substituting y = `-3/2` in (1), We have
`1/x - 2/3 = 4/3`

⇒ `1/x = 6/3 = 2`

⇒ x = `1/2`
Hence, x = `1/2   and y = - 3/2`