For what value of p will the pair of linear equations have infinitely many solutions (p-3)x + 3y = p , px+ py = 12

 p = 6

Step-by-step explanation:

HI !

 px + 3y - ( p-3)=0

a₁ = p , b₁ = 3 , c₁ = - (p-3)

12x + py - p=0

a₂ = 12  , b₂ = p , c₂ = -p

since , the equations have infinite solutions , 

a₁/a₂ = b₁/b₂ = c₁/c₂

p/12 = 3/p =  p-3/p

p/12 = 3/p

cross multiply ,

p² = 36

p = √36

 p = 6

for the value of p = 6 , the equations will have infinitely many solutions