In geometry, coincident lines are lines that lie exactly on top of each other. Visually, they look like a single line. In algebra (Class 10 Maths), they represent a pair of linear equations that have infinitely many solutions.
Coincident Lines: Lie on top of each other.
Algebraic Condition: a₁/a₂ = b₁/b₂ = c₁/c₂.
Solutions: Infinitely many.
System Type: Consistent and dependent.
In a pair of linear equations: a₁x + b₁y + c₁ = 0 a₂x + b₂y + c₂ = 0
The lines are coincident if the ratio of all their coefficients is exactly the same: a₁/a₂ = b₁/b₂ = c₁/c₂
| Type of Lines | Condition | Solutions |
|---|---|---|
| Intersecting | a₁/a₂ ≠ b₁/b₂ | Exactly 1 solution |
| Parallel | a₁/a₂ = b₁/b₂ ≠ c₁/c₂ | No solution |
| Coincident | a₁/a₂ = b₁/b₂ = c₁/c₂ | Infinitely many |
Coincident lines are two or more lines that lie exactly on top of each other, sharing all their points.
For equations a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, the condition is a₁/a₂ = b₁/b₂ = c₁/c₂.
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