If two lines intersect at one point on a graph, what is the pair called?
Answer and explanation
Correct answer: Consistent and independent
Two linear equations are represented by two straight lines on a graph. If the lines meet at exactly one point, that point satisfies both equations. Therefore, the pair has one and only one ordered pair as its solution. Such a pair is called consistent because at least one solution exists, and independent because the solution is unique.
Hence the correct description is “consistent and independent,” option C. Parallel distinct lines have no common point and represent an inconsistent pair. Coincident lines have infinitely many common points and represent a consistent dependent pair. Since the question states that the lines intersect at one point, neither of those alternatives applies.
Frequently asked questions
What is the correct answer to this question?
Consistent and independent
Why is this the correct answer?
Two linear equations are represented by two straight lines on a graph. If the lines meet at exactly one point, that point satisfies both equations. Therefore, the pair has one and only one ordered pair as its solution. Such a pair is called consistent because at least one solution exists, and independent because the solution is unique.
Hence the correct description is “consistent and independent,” option C. Parallel distinct lines have no common point and represent an inconsistent pair. Coincident lines have infinitely many common points and represent a consistent dependent pair. Since the question states that the lines intersect at one point, neither of those alternatives applies.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
