If the two lines are 4x + 2y = 10 and 2x + y = 5, what will be their position on the graph?
Answer and explanation
Correct answer: Coincident lines
The governing concept is comparing two linear equations after reducing them to a common standard form. Divide every term of the first equation 4x + 2y = 10 by 2. This gives 2x + y = 5, which is exactly the second equation. Therefore both equations describe the same set of points and represent one line drawn twice. Such lines are coincident and have infinitely many common solutions, so option D is correct. Parallel lines would have proportional x and y coefficients but different constants, intersecting lines would have different slopes, and perpendicularity is not indicated here. Scalar simplification proves coincidence directly.
Frequently asked questions
What is the correct answer to this question?
Coincident lines
Why is this the correct answer?
The governing concept is comparing two linear equations after reducing them to a common standard form. Divide every term of the first equation 4x + 2y = 10 by 2. This gives 2x + y = 5, which is exactly the second equation. Therefore both equations describe the same set of points and represent one line drawn twice. Such lines are coincident and have infinitely many common solutions, so option D is correct. Parallel lines would have proportional x and y coefficients but different constants, intersecting lines would have different slopes, and perpendicularity is not indicated here. Scalar simplification proves coincidence directly.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
