Question

If `2/x + 3/y = 13` and `5/x - 4/y = -2` then (x, y) is equal to ______.

Options

• `(1/2, 1/3)`

• `(1/3, 1/2)`

• `(1/2, -1/3)`

• `(1/3, -1/2)`

Answer 1

If `2/x + 3/y = 13` and `5/x - 4/y = -2` then (x, y) is equal to `underlinebb((1/2, 1/3)`.

Explanation:

Given the system of equations:

`2/x + 3/y = 13`

`5/x - 4/y = -2`

Let `(1/x = p)` and `(1/y = q)`.

Then the equations become:

2p + 3q = 13

5p – 4q = –2

Solving this system:

Multiply the first equation by 4:

8p + 12q = 52

Multiply the second equation by 3:

15p – 12q = –6

Add the two equations:

(8p + 15p) + (12q – 12q) = 52 – 6 

23p = 46

⇒ p = 2

Put (p = 2) back into the first equation: 

2(2) + 3q = 13 

⇒ 4 + 3q = 13

⇒ 3q = 9

⇒ q = 3

Recall that `(p = 1/x)` and `(q = 1/y)`, 

Thus, `x = 1/p = 1/2`, `y = 1/q = 1/3`.

Hence, `(x, y) = (1/2, 1/3)`.