If two lines have the same slope but different y-intercepts, how many solutions will the corresponding pair have?
Answer and explanation
Correct answer: No solution
The slope of a line determines its direction, while the y-intercept determines where it crosses the y-axis. Two lines with the same slope are parallel in direction. If their y-intercepts are different, they are distinct parallel lines, not the same line. Distinct parallel lines never meet at a common point, so there is no ordered pair (x, y) satisfying both equations simultaneously. Therefore the pair has no solution, and option B is correct. If both slope and y-intercept were the same, the lines would coincide and have infinitely many solutions; if the slopes differed, they would intersect once and have a unique solution.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
The slope of a line determines its direction, while the y-intercept determines where it crosses the y-axis. Two lines with the same slope are parallel in direction. If their y-intercepts are different, they are distinct parallel lines, not the same line. Distinct parallel lines never meet at a common point, so there is no ordered pair (x, y) satisfying both equations simultaneously. Therefore the pair has no solution, and option B is correct. If both slope and y-intercept were the same, the lines would coincide and have infinitely many solutions; if the slopes differed, they would intersect once and have a unique solution.
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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