(Q.21). For what positive values of ‘p’ the following pair of linear equations have infinitely many solutions?

px + 3y – (p – 3) = 0

12x + py – p = 0

Given: px + 3y – (p – 3) = 0

12x + py – p = 0

The above equations to have many solutions

a1
a2
 =
b1
b2
 =
c1
c2
∴
=
=
(p - )
⇒
p
12
 =
3
p

p. = ×

⇒ 2 =

⇒ p = ±