In which situation does graphical method give infinitely many solutions?
Answer and explanation
Correct answer: When lines are the same line
A pair of linear equations is represented by two straight lines. A solution is a point that lies on both lines at the same time. If the two equations produce exactly the same line, every point on that line belongs to both graphs. Consequently, every one of those points satisfies both equations.
Since a straight line contains infinitely many points, the pair has infinitely many common solutions. Therefore, option B, “when the lines are the same line,” is correct. Distinct parallel lines never meet and give no solution, while ordinary intersecting lines meet at one point and give one solution. Merely cutting the axes does not determine the number of common solutions.
Frequently asked questions
What is the correct answer to this question?
When lines are the same line
Why is this the correct answer?
A pair of linear equations is represented by two straight lines. A solution is a point that lies on both lines at the same time. If the two equations produce exactly the same line, every point on that line belongs to both graphs. Consequently, every one of those points satisfies both equations.
Since a straight line contains infinitely many points, the pair has infinitely many common solutions. Therefore, option B, “when the lines are the same line,” is correct. Distinct parallel lines never meet and give no solution, while ordinary intersecting lines meet at one point and give one solution. Merely cutting the axes does not determine the number of common 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: Graphical method of finding solutions..
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