Question

The condition for the pair of equations ax + by + c = 0 and px + qy + r = 0 to represent coinciding lines is
a / p ≠ b/ q
a / p = b/ q ≠ c/r
a / p = b/ q = c/r
a / p ≠ c/ r

Answer 1

Given,

The pair of equations ax + by + c = 0 and px + qy + c = 0.

To find,

condition of coinciding lines.

if two equations are a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 given

1. for unique solution ⇒a₁/a₂ ≠ b₁/b₂
2. for infinite solutions ⇒a₁/a₂ = b₁/b₂ = c₁/c₂
3. for no solution⇒a₁/a₂ = b₁/b₂ ≠ c₁/c₂

we know, coinciding lines means there are infinite solutions. so, 2nd condition will be applied.

here a₁ = a , a₂ = p, b₁ = b , b₂ = q , c₁ = c and c₂ = r.

so, a/p = b/q = c/r

therefore the condition of coinciding lines is a/p = b/q = c/r

Answer 2

Answer:

ni aata

Step-by-step explanation:

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