Question

Solve the following pairs of equations by reducing them to a pair of linear equations

`2/sqrtx +3/sqrty = 2`

`4/sqrtx - 9/sqrty = -1`

Answer 1

`2/sqrtx +3/sqrty = 2`

`4/sqrtx - 9/sqrty = -1`

Let `1/sqrtx = p ` , then the equations changes as below:

2p + 3q = 2 ... (i)

4p - 9q = -1 ... (ii)

Multiplying equation (i) by 3, we get

6p + 9q = 6 ... (iii)

Adding equation (ii) and (iii), we get

10p = 5

p = 1/2 ... (iv)

Putting in equation (i), we get

`2 × 1/2 + 3q = 2`

3q = 1

`q = 1/3`

`p = 1/sqrtx = 1/2`

`sqrtx = 2`

x = 4 and q = `1/sqrty = 1/3`

`sqrty = 3`

y = 9

Hence, x = 4, y = 9