If a pair of linear equations is consistent, then the lines representing them will be:
Parallel
Always coincident
Intersecting or coincident
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).
Stepwise Solution:
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]
Marking Scheme:
• Recalling definition of consistent system: 0.5 Mark
• Selecting intersecting or coincident: 0.5 Mark
Correct Answer: Intersecting or coincident