Question

If the graphs of two linear equations are parallel then the number of solutions will be

• A. 1
• B. 2
• C. infinitely many
• D. none of these

Hint:

Geometrically, solving a system of two linear equations means finding where the two lines cross. - Intersecting lines = 1 solution - Parallel lines = 0 solutions - Coincident (same) line = Infinite solutions

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The solutions to a system of linear equations correspond to the points of intersection of their graphs.

Step 2: Detailed Explanation:
Parallel lines are lines in a plane that never intersect, no matter how far they are extended.
Since they never meet, there are no common points that satisfy both equations simultaneously.
Therefore, a system of linear equations whose graphs are parallel has zero solutions (or no solution).
Let's analyze the given options:
(A) 1: This corresponds to intersecting lines.
(B) 2: A system of two linear equations cannot have exactly two solutions.
(C) infinitely many: This corresponds to coincident lines.
(D) none of these: Since the correct answer is 0 (no solution), and 0 is not listed in options A, B, or C, this option is the correct choice.

Step 3: Final Answer:
The number of solutions is zero. As this is not an option, the correct answer is none of these.