Question

Solve the following pair of equations:

`1/(2x) - 1/y = -1, 1/x + 1/(2y) = 8, x, y ≠ 0`

Answer 1

Given pair of linear equations are

`1/(2x) - 1/y` = – 1  ......(i)

And `1/x + 1/(2y)` = 8, x, y ≠ 0    ......(ii)

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

Then the above equations become

`u/2 - v` = – 1

⇒ u – 2v = – 2  ....(iii)

And `u + v/2` = 8

⇒ 2u + v = 16  .....(iv)

On multiplying equation (iv) by 2 and then adding with equation (iii), we get

4u + 2v = 32
  u – 2v = – 2
        5u = 30

⇒ u = 6

Now, put the value of u in equation (iv), we get

2 × 6 + v = 16

⇒ v = 16 – 12 = 4

⇒ v = 4

∴ x = `1/u = 1/6`

And y = `1/v = 1/4`

Hence the required values of x and y are `1/6` and `1/4`, respectively.