No solution and parallel lines
A pair of linear equations has no solution when the two lines are parallel and never meet.
Practice This ConceptMain explanation
Teacher explanation
Parallel lines stay at the same distance apart and do not intersect. Since no point is common to both lines, there is no ordered pair that satisfies both equations together. This is an important case in consistency questions and graph-based answers.
Example
The lines x + y = 3 and x + y = 7 are parallel. They have the same left side pattern but different constants, so they do not meet.
Simple analogy
Same slope, different intercepts, no meeting point.
Common confusion
Students often think parallel lines can meet after extension, but in Euclidean geometry they never intersect.
Exam tip
When a1/a2 = b1/b2 but is not equal to c1/c2, the pair has no solution.
Answer writing and exam use
1-mark use
Write the exact meaning of no solution and parallel lines in one clean line.
2-mark use
Define no solution and parallel lines and add one example or condition.
3-mark use
Explain no solution and parallel lines, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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