The number of solutions given by a pair of coincident lines

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Simple solution

Definite solution

Finite solution

Infinite solution

answer is D.

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Detailed Solution

Given a pair of coincident lines.
Coincident lines: - Two lines or shapes that lie exactly on top of each other.
A pair of the coincident lines has infinite solutions,
If pair of linear equation is given by

a 1 x + b 1 y + c 1 = 0

and

a 2 x + b 2 y + c 2 = 0

, then the following situations can arise,

a 1 b 1 = a 2 b 2 = c 1 c 2

In this case, the pair of the linear equation has infinitely many solutions (consistent pair of equations). It is the graphical representation of a coincident line and algebraically it is an infinite solution.
The number of solutions given by a pair of coincident lines is an infinite solution.
Therefore, the correct option is 4.

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