By observing the equations 18x + 5y = 79 and 36x + 10y = 158, which statement is correct?
Answer and explanation
Correct answer: The lines are the same
Multiply the first equation, 18x + 5y = 79, by 2. It becomes 36x + 10y = 158, exactly the second equation. Thus both equations have the same graph and represent one coincident line. The phrase “the lines are the same” is therefore the most precise statement; such a pair has infinitely many solutions. Distinct parallel lines would have proportional x and y coefficients but a different constant ratio, while intersecting lines would not have proportional coefficients.
Frequently asked questions
What is the correct answer to this question?
The lines are the same
Why is this the correct answer?
Multiply the first equation, 18x + 5y = 79, by 2. It becomes 36x + 10y = 158, exactly the second equation. Thus both equations have the same graph and represent one coincident line. The phrase “the lines are the same” is therefore the most precise statement; such a pair has infinitely many solutions. Distinct parallel lines would have proportional x and y coefficients but a different constant ratio, while intersecting lines would not have proportional coefficients.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
