Unique solution and intersecting lines
A pair of linear equations has a unique solution when the two lines intersect at exactly one point.
Practice This ConceptMain explanation
Teacher explanation
When two lines cross at one point, that point is the only ordered pair that satisfies both equations. This happens when the equations are consistent and independent. In algebraic form, the coefficients do not make the equations multiples of each other.
Example
The equations x + y = 5 and x - y = 1 intersect at one point, so they have a unique solution.
Simple analogy
One crossing point means one answer pair.
Common confusion
Students may confuse intersecting lines with parallel lines, especially when the graph is drawn approximately.
Exam tip
If the two lines meet once, write the intersection point as the final answer and check it in both equations.
Answer writing and exam use
1-mark use
Write the exact meaning of unique solution and intersecting lines in one clean line.
2-mark use
Define unique solution and intersecting lines and add one example or condition.
3-mark use
Explain unique solution and intersecting 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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