Question

Solve the following systems of 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 and `1/sqrty` = q

The given equations reduce to:

2p + 3q = 2  ....(1)

4p – 9q = –1  ....(2)

Multiplying equation (1) by (3), we obtain:

6p + 9q = 6  ....(3)

Adding equation (2) and (3), we obtain:

10p = 5

p = `1/2`

Putting the value of p in equation (1), we obtain:

`2 xx 1/2 + 3q = 2`

3q = 1

q = `1/3`

∴ p = `1/sqrtx = 1/2`

`sqrtx` = 2

x  = 4

q = `1/sqrty = 1/3`

`sqrty` = 3

y = 9

∴ x = 4, y = 9