If two lines have the same slope but different intercepts, what is the correct conclusion?
Answer and explanation
Correct answer: No solution
For a line y = mx + c, the value m fixes its direction and c fixes its vertical position. Equal slopes mean the two lines point in the same direction. Because their intercepts are different, they occupy different positions and cannot be the same line. They are therefore distinct parallel lines. Distinct parallel lines do not intersect, so there is no ordered pair (x, y) satisfying both equations at once. This is the condition of an inconsistent pair, and option B is correct. A unique solution would result from two lines with different slopes. Infinitely many solutions and coincident lines would require both slope and intercept to be equal, not just the slopes.
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What is the correct answer to this question?
No solution
Why is this the correct answer?
For a line y = mx + c, the value m fixes its direction and c fixes its vertical position. Equal slopes mean the two lines point in the same direction. Because their intercepts are different, they occupy different positions and cannot be the same line. They are therefore distinct parallel lines. Distinct parallel lines do not intersect, so there is no ordered pair (x, y) satisfying both equations at once. This is the condition of an inconsistent pair, and option B is correct. A unique solution would result from two lines with different slopes. Infinitely many solutions and coincident lines would require both slope and intercept to be equal, not just the slopes.
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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