If two lines have the same slope but different intercepts then what type of pair will it be?
Answer and explanation
Correct answer: Inconsistent
The governing graphical idea is that lines with the same slope are parallel, unless they also have the same intercept. Different intercepts mean the lines are distinct: they never meet at a common point. Therefore no ordered pair (x,y) can satisfy both equations at once, so the pair has no solution. A pair with no common solution is called inconsistent. Option A and option D refer to coincident lines, which have infinitely many common points, while option C refers to two non-parallel lines that intersect once. Thus the correct classification is inconsistent, option B.
Frequently asked questions
What is the correct answer to this question?
Inconsistent
Why is this the correct answer?
The governing graphical idea is that lines with the same slope are parallel, unless they also have the same intercept. Different intercepts mean the lines are distinct: they never meet at a common point. Therefore no ordered pair (x,y) can satisfy both equations at once, so the pair has no solution. A pair with no common solution is called inconsistent. Option A and option D refer to coincident lines, which have infinitely many common points, while option C refers to two non-parallel lines that intersect once. Thus the correct classification is inconsistent, option B.
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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