If two lines have different slopes, which statement is correct?
Answer and explanation
Correct answer: The pair is consistent and independent with one unique solution
Two lines with different slopes cannot be parallel or coincident, so they intersect at exactly one point. Hence, the pair of linear equations is consistent and independent and has one unique solution. Options B and D describe infinitely many solutions, which occur for coincident lines having the same slope. Exam tip: different slopes imply one unique solution; equal slopes with different intercepts imply no solution; and equal slopes with equal intercepts imply infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
The pair is consistent and independent with one unique solution
Why is this the correct answer?
Two lines with different slopes cannot be parallel or coincident, so they intersect at exactly one point. Hence, the pair of linear equations is consistent and independent and has one unique solution. Options B and D describe infinitely many solutions, which occur for coincident lines having the same slope. Exam tip: different slopes imply one unique solution; equal slopes with different intercepts imply no solution; and equal slopes with equal intercepts imply infinitely many solutions.
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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