Question

Solve the following pairs of equations by reducing them to a pair of linear equations

`(7x-2y)/(xy) = 5`

`(8x + 7y)/(xy) = 15`

Answer 1

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

`⇒ (7x)/(xy) - (2y)/(xy) = 5`

`⇒ 7/y - 2/x = 5 ... (i)`

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

`⇒ (8x)/(xy) + (7y)/(xy) = 15`

`⇒ 8/y + 7/x = 15 ... (ii)`

Putting `1/x = p ` in (i) and (ii) we get,

7q - 2p = 5 ... (iii)

8q + 7p = 15 ... (iv)

Multiplying equation (iii) by 7 and multiplying equation (iv) by 2 we get,

49q - 14p = 35 ... (v)

16q + 14p = 30 ... (vi)

Now, adding equation (v) and (vi) we get,

49q - 14p + 16q + 14p = 35 + 30

⇒ 65q = 65

⇒ q = 1

Putting the value of q in equation (iv)

8 + 7p = 15

⇒ 7p = 7

⇒ p = 1

Now,

p = 1/x = 1

⇒ 1/x = 1

⇒ x = 1

also, q = 1 = 1/y

⇒ 1/y = 1

⇒ y = 1

Hence, x =1 and y = 1 is the solution