If both lines appear exactly at the same place on the graph, how many solutions will there be?
Answer and explanation
Correct answer: Infinitely many solutions
The governing concept is the graphical classification of a pair of linear equations. If both graphs lie exactly on the same line, they are coincident lines. Every point on that common line satisfies the first equation and the second equation, so the pair has infinitely many common ordered pairs and therefore infinitely many solutions. Option B is correct. Intersecting lines meet at one point and produce one solution, whereas parallel distinct lines never meet and produce no solution. Two solutions are not possible for a pair of linear equations in two variables when the lines coincide; the common points are not limited to two. Algebraically, the equations are dependent and one equation is a scalar multiple of the other.
Frequently asked questions
What is the correct answer to this question?
Infinitely many solutions
Why is this the correct answer?
The governing concept is the graphical classification of a pair of linear equations. If both graphs lie exactly on the same line, they are coincident lines. Every point on that common line satisfies the first equation and the second equation, so the pair has infinitely many common ordered pairs and therefore infinitely many solutions. Option B is correct. Intersecting lines meet at one point and produce one solution, whereas parallel distinct lines never meet and produce no solution. Two solutions are not possible for a pair of linear equations in two variables when the lines coincide; the common points are not limited to two. Algebraically, the equations are dependent and one equation is a scalar multiple of the other.
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.
