Question

If `3/(x + y) + 2/(x - y) = 2` and `9/(x + y) - 4/(x - y) = 1` then

Options

• `x = 1/2, y = 3/2`

• `x = 5/2, y = 1/2`

• `x = 3/2, y = 1/2`

• `x = 1/2, y = 5/2`

Answer 1

`bb(x = 5/2, y = 1/2)`

Explanation:

Put `u = 1/(x + y)` and `v = 1/(x - y)`. 

Then the system becomes 3u + 2v = 2 and 9u – 4v = 1.

Multiply the first by 2 and add to the second:

(6u + 4v) + (9u – 4v) = 4 + 1 

⇒ 15u = 5

⇒ `u = 1/3`

From 3u + 2v = 2

⇒ 1 + 2v = 2 

⇒ `v = 1/2`

So, x + y = 3 and x – y = 2.

⇒ `x = (3 + 2)/2 = 5/2, y = (3 - 2)/2 = 1/2`