Question

For what value of p the pair of equations 2x+py=-5 and 3x+3y=-6 has a unique solution

Answer 1

P should not be equal to 3
If p=3 then the lines become parallel then there will be no solution
To have unique solution p should not be equal to 3

Answer 2

HI !

2x + py = -5 => 2x + py + 5 = 0

a₁ = 2 , b₁= p , c₁ = 5
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3x + 3y = -6  => 3x + 3y + 6 = 0

a₂ = 3 , b₂ = 3  , c₂ = 6

As they have unique solution ,

a₁/a² ≠ b₁/b₂

2/3 ≠ p/3

3p ≠ 6

p ≠ 3

the pair of equations will have unique solution , for all values of p except 3