What type of solution is given by the lines 2x − 5y = 1 and 6x − 15y = 3?
Answer and explanation
Correct answer: Infinitely many solutions
The second equation is obtained by multiplying every term of the first equation by 3: 3(2x − 5y = 1) gives 6x − 15y = 3. Therefore, both equations represent the same line. In ratio form, 6/2 = (−15)/(−5) = 3/1 = 3, confirming that all three ratios are equal. Coincident lines have infinitely many common points, so the pair has infinitely many solutions. Two linear equations cannot have exactly two isolated intersection points.
Frequently asked questions
What is the correct answer to this question?
Infinitely many solutions
Why is this the correct answer?
The second equation is obtained by multiplying every term of the first equation by 3: 3(2x − 5y = 1) gives 6x − 15y = 3. Therefore, both equations represent the same line. In ratio form, 6/2 = (−15)/(−5) = 3/1 = 3, confirming that all three ratios are equal. Coincident lines have infinitely many common points, so the pair has infinitely many solutions. Two linear equations cannot have exactly two isolated intersection points.
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.
