If both lines on a graph form exactly the same line, how many solutions will there be?
Answer and explanation
Correct answer: Infinitely many solutions
A solution of two linear equations is a point that lies on both corresponding lines. When the graphs are exactly the same line, every point drawn on that line belongs to both graphs. Hence every one of those points satisfies both equations, rather than just one specially selected point.
Because a straight line contains infinitely many points, the equations have infinitely many common solutions. Therefore, option B is correct. One point of intersection would indicate a unique solution, which occurs for non-parallel lines that meet once. Distinct parallel lines have no common point and therefore no solution. The possibilities “only two” and “one” do not describe coincident lines.
Frequently asked questions
What is the correct answer to this question?
Infinitely many solutions
Why is this the correct answer?
A solution of two linear equations is a point that lies on both corresponding lines. When the graphs are exactly the same line, every point drawn on that line belongs to both graphs. Hence every one of those points satisfies both equations, rather than just one specially selected point.
Because a straight line contains infinitely many points, the equations have infinitely many common solutions. Therefore, option B is correct. One point of intersection would indicate a unique solution, which occurs for non-parallel lines that meet once. Distinct parallel lines have no common point and therefore no solution. The possibilities “only two” and “one” do not describe 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..
