(Q6).Solve each of the following pairs of equations by reducing them to a pair of linear equations.

2
√x
 +
3
√y
 = 2;
4
√x
 -
9
√y
 = -1

Given

2
√x
 +
3
√y
 = 2 and
4
√x
 -
9
√y
 = -1
Take
1
√x
 = and
1
√y
 = ,

then the given equations reduces to

a + b = 2 …….. (1)

a – b = – 1 …….. (2)

equation (1) × ⇒ a + b =
equation (2)        ⇒ a - b = -
b =
⇒ b =
=
1
Substituting b =
1
 in equation (1) we get
2a + 3 (
1
 ) = 2
⇒ 2a + = 2 ⇒ 2a = 2 – ⇒ a =
but a =
1
√x
 =
1

⇒ √x = ⇒ (√x)2 = 2 ⇒ x =

b =
1
√y
 =
1

⇒ √y = ⇒ (√y)2 = 2

⇒ y =

∴ Solution (x, y) = (, )