If two lines have the same slope and the same intercept then how many solutions will there be?
Answer and explanation
Correct answer: Infinitely many solutions
A line is determined by its slope and its y-intercept. If two lines have the same slope and the same y-intercept, they occupy exactly the same position on the coordinate plane. They are not two different lines; they are coincident lines. Consequently, every point on that common line satisfies both equations.
Since every point of the line is a common solution, the pair does not have just one or two solutions. It has infinitely many solutions. In the usual classification, this is called a consistent and dependent pair. “No solution” would describe distinct parallel lines, which have the same slope but different intercepts. Therefore option C, infinitely many solutions, is correct.
Frequently asked questions
What is the correct answer to this question?
Infinitely many solutions
Why is this the correct answer?
A line is determined by its slope and its y-intercept. If two lines have the same slope and the same y-intercept, they occupy exactly the same position on the coordinate plane. They are not two different lines; they are coincident lines. Consequently, every point on that common line satisfies both equations.
Since every point of the line is a common solution, the pair does not have just one or two solutions. It has infinitely many solutions. In the usual classification, this is called a consistent and dependent pair. “No solution” would describe distinct parallel lines, which have the same slope but different intercepts. Therefore option C, infinitely many solutions, 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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