If two lines have different slopes, which conclusion is correct for their pair?
Answer and explanation
Correct answer: Unique solution
The slope tells us how steep a line is. If two lines have different slopes, they cannot remain parallel and they cannot be the same line. Their directions are different, so they meet at one and only one point. Therefore, the pair of linear equations is consistent and independent, and it has a unique solution. The correct choice is C, “Unique solution.”
In the graph, the common point gives the values of both variables simultaneously. Choice A would apply to distinct parallel lines, which have equal slopes and never meet. Choice B and choice D describe coincident, or dependent, lines; such lines have the same slope and share infinitely many points. Since the slopes here are different, exactly one intersection is possible, so C follows directly.
Frequently asked questions
What is the correct answer to this question?
Unique solution
Why is this the correct answer?
The slope tells us how steep a line is. If two lines have different slopes, they cannot remain parallel and they cannot be the same line. Their directions are different, so they meet at one and only one point. Therefore, the pair of linear equations is consistent and independent, and it has a unique solution. The correct choice is C, “Unique solution.”
In the graph, the common point gives the values of both variables simultaneously. Choice A would apply to distinct parallel lines, which have equal slopes and never meet. Choice B and choice D describe coincident, or dependent, lines; such lines have the same slope and share infinitely many points. Since the slopes here are different, exactly one intersection is possible, so C 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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