For the lines y = 3 and y = 11, how many solutions will there be?
Answer and explanation
Correct answer: No solution
The governing concept is the number of common points of two graphs. An equation y = a represents a horizontal line because the y-coordinate is fixed while x may take any value. Therefore y = 3 and y = 11 are distinct horizontal lines. Since their y-values are different, no point can satisfy both equations at the same time: a common point would have to have y equal to 3 and 11 simultaneously. Hence the pair has no solution, so option B is correct. Coincident lines would give infinitely many solutions, while intersecting lines would give one solution; neither situation occurs here.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
The governing concept is the number of common points of two graphs. An equation y = a represents a horizontal line because the y-coordinate is fixed while x may take any value. Therefore y = 3 and y = 11 are distinct horizontal lines. Since their y-values are different, no point can satisfy both equations at the same time: a common point would have to have y equal to 3 and 11 simultaneously. Hence the pair has no solution, so option B is correct. Coincident lines would give infinitely many solutions, while intersecting lines would give one solution; neither situation occurs here.
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..
