For infinitely many solutions of 3x + ny = 18 and 5x + 10y = 30, what is n?
Answer and explanation
Correct answer: n = 6
Infinitely many solutions require the equations to be proportional. Therefore, 3/5 = n/10 = 18/30. The first and third ratios both equal 3/5. Hence n/10 = 3/5, and multiplying by 10 gives n = 6. Verification confirms that 3/5 = 6/10 = 18/30. Thus option C is correct. If n were 4, 5, or 8, the y-coefficient ratio would not equal the x-coefficient and constant ratios, so the two equations would not represent the same line and could not have infinitely many common solutions.
Frequently asked questions
What is the correct answer to this question?
n = 6
Why is this the correct answer?
Infinitely many solutions require the equations to be proportional. Therefore, 3/5 = n/10 = 18/30. The first and third ratios both equal 3/5. Hence n/10 = 3/5, and multiplying by 10 gives n = 6. Verification confirms that 3/5 = 6/10 = 18/30. Thus option C is correct. If n were 4, 5, or 8, the y-coefficient ratio would not equal the x-coefficient and constant ratios, so the two equations would not represent the same line and could not have infinitely many common solutions.
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.
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