Question

`14/x + 3/y = 5, 21/x - 8/y = -5`

Answer 1

`14/x + 3/y = 5`     ...(i)

`21/x - 8/y = -5`     ...(ii)

Let,

`1/x = a and 1/y = b`

Substitute into the equation,

14a + 3b = 5     ...(iii)

21a − 8b = −5     ...(iv)

Now, solving equations (iii) and (iv) using the method of elimination:

Multiply (iii) by 8:

8(14a + 3b) = 8(5)

112a + 24b = 40     ...(v)

Multiply (iv) by 3:

3(21a − 8b) = 3(−5)

63a − 24b = −15     ...(vi)

Adding equation (v) and equation (vi):

(112a + 24b) + (63a − 24b) = 40 + (−15)

112a + 63a = 25

175a = 25

a = `25/175`

∴ a = `1/7`

Substitute a = `1/7` into (iii):

`14(1/7) + 3b = 5`

2 + 3b = 5

3b = 5 − 2

3b = 3

b = `3/3`

∴ b = 1

So, `1/x = a`

`1/x = 1/7`

∴ x = 7

Also, `1/y = b`

`1/y = 1`

∴ y = 1