If two lines have the same slope but different y-intercepts, which conclusion is correct?
Answer and explanation
Correct answer: No solution
A line written as y = mx + c has slope m and y-intercept c. If two lines have the same m, they have the same direction and are parallel unless their intercepts are also equal. Different y-intercepts place the lines at different vertical positions, so they are distinct parallel lines. Distinct parallel lines never meet at a common point; therefore the associated pair of linear equations has no solution. A unique solution would require intersecting lines, while infinitely many solutions would require coincident lines with both the same slope and the same intercept. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
A line written as y = mx + c has slope m and y-intercept c. If two lines have the same m, they have the same direction and are parallel unless their intercepts are also equal. Different y-intercepts place the lines at different vertical positions, so they are distinct parallel lines. Distinct parallel lines never meet at a common point; therefore the associated pair of linear equations has no solution. A unique solution would require intersecting lines, while infinitely many solutions would require coincident lines with both the same slope and the same intercept. Hence option B is correct.
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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