Question

solve this by reducinh them to apair of linear equations

Answer 1

Hey

Here is your answer,

2/√x +3/√y = 2
4/√x - 9/√y = -1
Let 1/√x = p and 1/√y = q, 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/√x = 1/2
√x = 2
x = 4
and
q = 1/√y = 1/3
√y = 3
y = 9
Hence, x = 4, y = 9

Hope it helps you!