If two lines intersect at exactly one point in a graph then what is the solution type?
Answer and explanation
Correct answer: One unique solution
In the graphical method, a solution of a pair of linear equations is represented by a common point of the two graphs. If the two lines intersect at exactly one point, only the coordinates of that point satisfy both equations simultaneously. Therefore the pair has exactly one solution, called a unique solution. In standard terminology, the pair is consistent and independent. No solution occurs when distinct lines are parallel, while infinitely many solutions occur when the two equations represent the same coincident line. “Inconsistent” is another name for the no-solution case, so it cannot describe a pair that intersects once. Hence option B is correct.
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What is the correct answer to this question?
One unique solution
Why is this the correct answer?
In the graphical method, a solution of a pair of linear equations is represented by a common point of the two graphs. If the two lines intersect at exactly one point, only the coordinates of that point satisfy both equations simultaneously. Therefore the pair has exactly one solution, called a unique solution. In standard terminology, the pair is consistent and independent. No solution occurs when distinct lines are parallel, while infinitely many solutions occur when the two equations represent the same coincident line. “Inconsistent” is another name for the no-solution case, so it cannot describe a pair that intersects once. 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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