Question

For what positive values of “P” the following pair of linear
equations have infinitely many solutions?
Px + 3y – (p – 3) = 0 12x + py – p = 0​

Answer 1

Answer:

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Answer 2

Given :  Px + 3y – (P – 3) = 0  and 12x + Py – P = 0​

To find :Value of P so that linear equations have infinitely many solutions

Solution:

Px + 3y – (P – 3) = 0

12x + Py – P = 0​

Two Equations are Consistent and have infinite many solutions  

a₁x  + b₁y  +  c₁ =0

a₂x + b₂y + c₂ = 0

if   a₁ / a₂  =  b₁/b₂  = c₁/c₂

=> P/12  =  3/P  =     -(P -3)/(-P)

=> P/12  =  3/P    => P² = 36  => P = ± 6

3/P  =   -(P -3)/(-P)

=> 3 = P - 3

=> P = 6

So P  = 6  is the only possible value

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