How many solutions are there in a consistent and independent pair?
Answer and explanation
Correct answer: One unique solution
The governing concept is the classification of a pair of linear equations by the relationship between their graphs. A consistent pair has at least one common solution, while an independent pair represents two different lines. Two different non-parallel lines intersect at exactly one point, and the coordinates of that intersection satisfy both equations simultaneously. Hence the pair has one and only one solution, called a unique solution. Option A describes parallel distinct lines, option B describes coincident lines, and option D is not a possible general classification for two linear equations in two variables.
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What is the correct answer to this question?
One unique solution
Why is this the correct answer?
The governing concept is the classification of a pair of linear equations by the relationship between their graphs. A consistent pair has at least one common solution, while an independent pair represents two different lines. Two different non-parallel lines intersect at exactly one point, and the coordinates of that intersection satisfy both equations simultaneously. Hence the pair has one and only one solution, called a unique solution. Option A describes parallel distinct lines, option B describes coincident lines, and option D is not a possible general classification for two linear equations in two variables.
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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