If (6x+5y=31) and (12x+10y=n) have infinitely many solutions, what is (n)?
Answer and explanation
Correct answer: 62
For two linear equations to have infinitely many solutions, one equation must be a constant multiple of the other. Here, the coefficients of x and y in the second equation are twice those in the first: 12=2×6 and 10=2×5. Therefore, the constant term must also be doubled, so n=2×31=62. Hence, option C is correct. Exam tip: For infinitely many solutions, check a₁/a₂=b₁/b₂=c₁/c₂.
Frequently asked questions
What is the correct answer to this question?
62
Why is this the correct answer?
For two linear equations to have infinitely many solutions, one equation must be a constant multiple of the other. Here, the coefficients of x and y in the second equation are twice those in the first: 12=2×6 and 10=2×5. Therefore, the constant term must also be doubled, so n=2×31=62. Hence, option C is correct. Exam tip: For infinitely many solutions, check a₁/a₂=b₁/b₂=c₁/c₂.
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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