(Q7).Solve each of the following pairs of equations by reducing them to a pair of linear equations.

6x + 3y = 6xy

2x + 4y = 5xy

Given

6x + 3y = 6xy

⇒
6x+3y
 = 6
⇒
6x
 +
3y
 = 6
⇒
6
 +
3
 = 6

2x + 4y = 5xy

⇒
2x+4y
 = 5
⇒
2x
 +
4y
 = 5
⇒
2
 +
4
 = 5
Take
1
x
 = and
1
y
 = ,

then the given equations reduces to

a + b = 6 ……. (1)

a + b = 5 ……. (2)

equation (1) × ⇒ a + b =
equation (2) × ⇒ a + b =
b =
⇒ b =
=
1
Substituting b =
1
 in equation (1) we get
3a + 6 (
1
 ) = 6

⇒ 3a = 6 –

⇒ a =
3
 =
but a =
1
x
 = ⇒ x =
b =
1
y
 =
1
 ⇒ y =

∴ Solution (x, y) = (, )