In which case is a pair of two linear equations called consistent?
Answer and explanation
Correct answer: When there is at least one solution
A pair of linear equations is called consistent when the two equations have at least one common solution. Geometrically, their graphs either meet at one point or lie on the same line. Thus, consistency does not require exactly one solution; a pair may also have infinitely many solutions.
For two lines, intersecting lines give one common point, while coincident lines give infinitely many common points. Both cases are consistent. Parallel distinct lines have no common point and are inconsistent. Therefore, option A is the complete and correct condition. The ratio statement in option D is not a general definition and cannot identify every consistent pair.
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What is the correct answer to this question?
When there is at least one solution
Why is this the correct answer?
A pair of linear equations is called consistent when the two equations have at least one common solution. Geometrically, their graphs either meet at one point or lie on the same line. Thus, consistency does not require exactly one solution; a pair may also have infinitely many solutions.
For two lines, intersecting lines give one common point, while coincident lines give infinitely many common points. Both cases are consistent. Parallel distinct lines have no common point and are inconsistent. Therefore, option A is the complete and correct condition. The ratio statement in option D is not a general definition and cannot identify every consistent pair.
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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