When does graphical method give infinitely many solutions?
Answer and explanation
Correct answer: When lines are the same line
In the graphical method, each linear equation is drawn as a straight line, and common solutions are the points shared by the two lines. If the lines are distinct and parallel, they never meet, so there is no common solution. If they cross at one point, there is exactly one solution.
Infinitely many solutions occur only when both equations represent the very same line. Then every point on that line is common to both graphs, and each such point satisfies both equations. Therefore, option B is correct. Cutting the coordinate axes does not by itself create infinitely many common solutions, and a single given point cannot represent all the solutions of a pair of coincident lines.
Frequently asked questions
What is the correct answer to this question?
When lines are the same line
Why is this the correct answer?
In the graphical method, each linear equation is drawn as a straight line, and common solutions are the points shared by the two lines. If the lines are distinct and parallel, they never meet, so there is no common solution. If they cross at one point, there is exactly one solution.
Infinitely many solutions occur only when both equations represent the very same line. Then every point on that line is common to both graphs, and each such point satisfies both equations. Therefore, option B is correct. Cutting the coordinate axes does not by itself create infinitely many common solutions, and a single given point cannot represent all the solutions of a pair of coincident lines.
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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