Question

If `1/x + 2/y = 4` and `3/y - 1/x = 11` then

Options

• x = 2, y = 3

• x = –2, y = 3

• `x = (-1)/2, y = 3`

• `x = (-1)/2, y = 1/3`

Answer 1

`bb(x = (-1)/2, y = 1/3)`

Explanation:

Let `u = 1/x` and `v = 1/y`.

Then the system becomes

u + 2v = 4

–u + 3v = 11

Add the equations: 

5v = 15

⇒ v = 3

Substitute into u + 2v = 4: 

u + 6 = 4

⇒ u = –2

So, `1/x = -2 ⇒ x = (-1)/2` and `1/y = 3 ⇒ y = 1/3`.