If (9x+5y=47) and (27x+15y=n) have infinitely many solutions, what is (n)?
Answer and explanation
Correct answer: 141
For two linear equations to have infinitely many solutions, the ratios of their corresponding coefficients and constants must be equal. Here, \(27/9=3\) and \(15/5=3\), so the second equation must be 3 times the first one. Hence, \(n=3\times47=141\), making option C correct. Exam tip: For infinitely many solutions, check \(a_1/a_2=b_1/b_2=c_1/c_2\).
Frequently asked questions
What is the correct answer to this question?
141
Why is this the correct answer?
For two linear equations to have infinitely many solutions, the ratios of their corresponding coefficients and constants must be equal. Here, \(27/9=3\) and \(15/5=3\), so the second equation must be 3 times the first one. Hence, \(n=3\times47=141\), making option C correct. Exam tip: For infinitely many solutions, check \(a_1/a_2=b_1/b_2=c_1/c_2\).
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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