Chapter 3 · Question 2
Explain the three graphical possibilities for a pair of linear equations.
Q2
Explain the three graphical possibilities for a pair of linear equations.
Answer Revealed
Direct Answer:
The two lines may intersect at one point, be parallel, or coincide. Intersecting lines give one solution; parallel lines give no solution; coincident lines give infinitely many solutions.
Simple Explanation
Two lines can cross, never meet, or lie exactly on each other. These mean one, no, or infinitely many solutions.
Exam-Ready Structure
Graphically, a pair of linear equations represents two lines. If the lines intersect, the pair is consistent and has a unique solution. If the lines are parallel, the pair is inconsistent and has no solution. If the lines coincide, the pair is dependent and has infinitely many solutions.
Key Points
- The two lines may intersect at one point, be parallel, or coincide.
- Use the NCERT formula or theorem carefully.
- Write units and final conclusion where applicable.