Question

For what positive values of p, the following pair of linear equations have infinite solutions
Px+3y-(p-3)=0
12x+py-p=0

Answer 1

Step-by-step explanation:

Given equation are

(p−3)x+3y=p

px+py=12

The pair of linear equation has infinitely many solutions.

a

2

a

1

=

b

2

b

1

=

c

2

c

1

p

p−3

=

p

3

=

12

p

a

2

a

1

=

c

2

c

1

p

p−3

=

12

p

(p−3)12=p

2

12p−36=p

2

p

2

−12p−36=0

p

2

−6p−6p−36=0

p(p−6)−6(p−6)=0

p−6=0

∴p=6.

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