Question

Solve the following system of equations:

`(xy)/(x + y) = 6/5`

`(xy)/(y - x) = 6`

Answer 1

The given system of equations is

`(xy)/(x + y) = 6/5`

⇒ 5xy = 6(x + y)

⇒ 5xy = 6x + 6y ....(i)

And `(xy)/(y - x) = 6`

⇒ xy = 6(y - x)

⇒ xy = 6y - 6x ....(ii)

Adding equation (i) and equation (ii), we get

 6xy = 6y + 6y

⇒ 6xy = 12y

`=> x = (12y)/(6y) = 2`

Putting x = 2 in equation (i), we get

`5 xx 1 xx y = 6 xx 2 + 6y`

⇒ 10y = 12 + 6y

⇒ 10y - 6y = 12

⇒ 4y = 12

`=> y = 12/4 = 3`

Hence, solution of the given system of equations is x = 2, y = 3.