Question

Find the values of p for which the following
pair of linear equations have a unique solution :
(3p + 1)x - py + 7 = 0
2px + y - 3 = 0

Answer 1

hear is the answer i hope this will help you find the answers based on this type questions

Answer 2

Given:

pair of linear equations :

(3p + 1)x - py + 7 = 0

2px + y - 3 = 0

they have unique solution

To Find:

The values of p for which the following

pair of linear equations has a unique solution.

Solution:

The condition for a unique solution is

⇒ a₁/a₂ ≠ b₁/b₂

so for eqn,

⇒ (3p + 1)x - py + 7 = 0

a₁ = ( 3p + 1) , b₁ = -p

⇒ 2px + y - 3 = 0

a₂ = 2p  , b₂ = 1

∴  a₁/a₂ ≠ b₁/b₂ ⇒ ( 3p + 1) /2p ≠ -p/1

⇒ ( 3p + 1)  ≠ -2p²

⇒ 2p² + 3p + 1 ≠ 0

⇒ 2p² + 2p + p + 1 ≠ 0

⇒ 2p ( p + 1 ) + 1 ( p + 1 ) ≠ 0

⇒  ( p + 1 ). ( 2p + 1 ) ≠ 0

⇒  ( p + 1 ) ≠ 0,       ( 2p + 1 ) ≠ 0

⇒ p ≠ -1 , -1/2

Hence, the value of p will be any real number except -1 and -1/2.