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 the 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