If two lines have the same slope and the same intercept, what will be the type of the pair?
Answer and explanation
Correct answer: Consistent and dependent
In slope-intercept form, a line is represented by y = mx + c, where m is the slope and c is the y-intercept. If two lines have the same slope and the same intercept, their equations describe exactly the same set of points. Thus the lines are coincident, not merely parallel. Every point on that common line satisfies both equations, so the pair has infinitely many solutions. Such a pair is called consistent because solutions exist, and dependent because one equation is a scalar multiple of the other. Therefore option C is correct. Options A and D describe no common solution, while option B would require intersecting lines and exactly one solution.
Frequently asked questions
What is the correct answer to this question?
Consistent and dependent
Why is this the correct answer?
In slope-intercept form, a line is represented by y = mx + c, where m is the slope and c is the y-intercept. If two lines have the same slope and the same intercept, their equations describe exactly the same set of points. Thus the lines are coincident, not merely parallel. Every point on that common line satisfies both equations, so the pair has infinitely many solutions. Such a pair is called consistent because solutions exist, and dependent because one equation is a scalar multiple of the other. Therefore option C is correct. Options A and D describe no common solution, while option B would require intersecting lines and exactly one 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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