Question

For what values of p does the pair of equations 4x + py + 8 =0 and 2x + 2y

+2 =0 have a unique solution?​

Answer 1

Answer:

if the pair of equations has a unique solution. (v) 2x + 3y = 7 and 2px + py = 28 -qy, if the pair of equations has infinitely many solutions. Therefore, the given pair of linear equations are parallel for all real values of p except 10.

Answer 2

Given Equation

⇒4x + py + 8 = 0

⇒2x + 2y + 2 = 0

To find the value p

We know that for unique solution

⇒a₁/a₂≠ b₁/b₂

Now compare with

⇒a₁x + b₁y + c₁ = 0

⇒a₂x + b₂y + c₂ = 0

We get

⇒a₁ = 4 , b₁ = p , c₁ = 8 , a₂ = 2 , b₂ = 2 and c₂ = 2

Now put the value on given condition

⇒4/2 ≠ p/2

⇒2 ≠ p/2

⇒p≠2×2

⇒p ≠ 4

Value of p all Real number except 4