Question

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

Answer 1

Answer: p = 6

Explanation:

HI !

px + 3y - ( p-3)=0

a₁ = p , b₁ = 3 , c₁ = - (p-3)

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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

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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