Question

If the graphs of two linear equations are coincident lines, then how many solutions do they have?

• A. One solution
• B. No solution
• C. Infinitely many solutions
• D. None of these

Hint:

Parallel distinct lines $\Rightarrow$ no solution; intersecting lines $\Rightarrow$ one solution; coincident lines $\Rightarrow$ infinitely many solutions.

Answer 1

The Correct Option is C

Step 1: Understand ``coincident lines.''
Two lines are coincident if they lie exactly on top of each other; every point on one line is also on the other.
Step 2: Interpret in terms of solutions.
A solution to a pair of linear equations corresponds to a point common to both lines.
Since coincident lines share {all} points, there are infinitely many common points (solutions).
Step 3: Conclusion.
Therefore, a system represented by coincident lines is consistent and dependent with infinitely many solutions.