If a pair of linear equations is consistent, then the lines representing them will be:
(a) Parallel
(b) Always coincident
(c) Intersecting or coincident
(d) Always intersecting
Step-by-Step Solution
Key Concept: Consistency means having at least one solution (intersecting lines have 1 solution, coincident lines have infinitely many).
A system is consistent if it has one or more solutions. [0.5 Mark]
Intersecting lines give a unique solution; coincident lines give infinitely many. Thus, consistent lines are intersecting or coincident. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Recalling definition of consistent system: 0.5 Mark
Selecting intersecting or coincident: 0.5 Mark
Correct Answer: Intersecting or coincident