If the lines of two equations are coincident, what is the pair called?
Answer and explanation
Correct answer: Consistent and dependent
Coincident lines are two equations that represent exactly the same straight line. Every point on that line satisfies both equations, so the pair has infinitely many common solutions. Because at least one common solution exists, the pair is consistent. Because the equations do not determine one unique point, it is also called dependent.
This gives the classification “consistent and dependent,” which is option B. An inconsistent pair would represent distinct parallel lines and have no common solution. A consistent independent pair would represent intersecting lines and have exactly one solution. Therefore, neither A nor C describes coincident lines, and option B follows directly.
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What is the correct answer to this question?
Consistent and dependent
Why is this the correct answer?
Coincident lines are two equations that represent exactly the same straight line. Every point on that line satisfies both equations, so the pair has infinitely many common solutions. Because at least one common solution exists, the pair is consistent. Because the equations do not determine one unique point, it is also called dependent.
This gives the classification “consistent and dependent,” which is option B. An inconsistent pair would represent distinct parallel lines and have no common solution. A consistent independent pair would represent intersecting lines and have exactly one solution. Therefore, neither A nor C describes coincident lines, and option B follows directly.
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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