Question

For which value (s) of p,do the pair of linear equations px+y=p square and x+py=1 have (i) no solution ?( ii) infinitely many solutions (iii) a unique solution.​

Answer 1

Answer:

The equations (p−3)x+3y−p=0

px+py−12=0

For infinite many solution

a

2

a

1

=

b

2

b

1

=

c

2

c

1

Here a

1

=p−3,b

1

=3,c

1

−p

a

2

=p,b

2

=p,c

2

=−12

p

p−3

=

p

3

=

−12

−1

Solving

p

3

=

−12

−1

⟹p

2

=36⟹p=±6

Now solving

p

p−3

=

−12

−1

⟹p−3=3⟹p=6

Hence the value of p=6.