Question

6.

For what value of p, does the pair of linear equations 4x + py = 8 and 2x + 2y = -2 has unique solution?​

Answer 1

The given pair of linear equation :

⇒ (p+2)x−(2p+1)y=3(2p−1) ------ ( 1 )

⇒ 2x−3y=7 ------- ( 2 )

On comparing with equations,

a

1

x+b

1

y+c

1

=0

and a

2

x+b

2

y+c

2

=0

We get, a

1

=(p+2),b

1

=−(2p+1),c=−[3(2p−1)]

a

2

=2,b

2

=−3,c=−7

⇒

a

2

a

1

=

2

p+2

and

b

2

b

1

=

−3

−(2p+1)

A pair of linear equations has a unique solution, if

⇒

a

2

a

1



=

b

2

b

1

⇒

2

(p+2)



=

−3

−(2p+1

⇒ −3(p+2)



=2(−2p−1)

⇒ −3p−6



=−4p−2

⇒ −3p+4p



=−2+6

⇒ p



=4

Therefore, the given system will have unique solution for all real values of p other than 4