Which conclusion is correct for the equations 9x − 2y = 31 and 27x − 6y = 93?
Answer and explanation
Correct answer: There are infinitely many solutions
The first equation is 9x − 2y = 31. Multiplying it by 3 produces 27x − 6y = 93, exactly the second equation. Therefore, the pair represents two coincident lines, not two intersecting or distinct parallel lines. The coefficient ratios also confirm this: 27/9 = (−6)/(−2) = 93/31 = 3. Every point satisfying the first equation automatically satisfies the second, so infinitely many solutions exist.
Frequently asked questions
What is the correct answer to this question?
There are infinitely many solutions
Why is this the correct answer?
The first equation is 9x − 2y = 31. Multiplying it by 3 produces 27x − 6y = 93, exactly the second equation. Therefore, the pair represents two coincident lines, not two intersecting or distinct parallel lines. The coefficient ratios also confirm this: 27/9 = (−6)/(−2) = 93/31 = 3. Every point satisfying the first equation automatically satisfies the second, so infinitely many solutions exist.
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.
