If two lines have the same slope and different (y)-intercepts, how many solutions will their pair of equations have?
Answer and explanation
Correct answer: No solution
Two lines with the same slope are either coincident or parallel. Different (y)-intercepts show that the lines are not coincident, so they are distinct parallel lines and never intersect. Hence, the pair of equations has no solution. Exam tip: equal slopes with different intercepts indicate no solution, whereas equal slopes with equal intercepts indicate infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
Two lines with the same slope are either coincident or parallel. Different (y)-intercepts show that the lines are not coincident, so they are distinct parallel lines and never intersect. Hence, the pair of equations has no solution. Exam tip: equal slopes with different intercepts indicate no solution, whereas equal slopes with equal intercepts indicate infinitely many solutions.
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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