If two lines completely overlap in a graph, how many solutions does the pair have?
Answer and explanation
Correct answer: Infinitely many solutions
The governing concept is the graphical classification of a pair of linear equations. When two lines completely overlap, they are called coincident lines. Every point on one line also lies on the other, so every such point satisfies both equations simultaneously. A line contains infinitely many points; consequently, the pair has infinitely many ordered-pair solutions. Thus option C is correct. Distinct parallel lines never meet and give no solution, while intersecting lines share exactly one point and give one solution. Option D is not a general description of a coincident pair because the common points need not lie on y = 0; they can lie anywhere on the common line.
Frequently asked questions
What is the correct answer to this question?
Infinitely many solutions
Why is this the correct answer?
The governing concept is the graphical classification of a pair of linear equations. When two lines completely overlap, they are called coincident lines. Every point on one line also lies on the other, so every such point satisfies both equations simultaneously. A line contains infinitely many points; consequently, the pair has infinitely many ordered-pair solutions. Thus option C is correct. Distinct parallel lines never meet and give no solution, while intersecting lines share exactly one point and give one solution. Option D is not a general description of a coincident pair because the common points need not lie on y = 0; they can lie anywhere on the common line.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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