Question

Solve the following systems of equations:

`(7x - 2y)/"xy" = 5`

`(8x + 7y)/"xy" = 15`

Answer 1

`(7x - 2y)/"xy" = 5`

`=> 7/y - 2/x = 5` .....(1)

`(8x + 7y)/(xy) = 15`

`=> 8/y + 7/x = 15` ..........(2)

Let `1/x = p and 1/y = q`

The given equations reduce to:

-2p + 7q = 5

=> -2p + 7q - 5 = 0 ...(3)

7p + 8q = 15

=> 7p + 8q - 15 = 0 ....(4)

Using cross multiplication method, we obtain:

`p/(-105-(-40)) = q/(-35-30) = 1/(-16-49)`

`p/(-65) = 1/(-65), q/(-65) = 1/(-65)`

p = 1, q= 1

`p = 1/x = 1, q= 1/y =1`

x = 1 , y = 1