What is the value of (q) for the equations (13x+qy=52) and (26x+18y=104) to have infinitely many solutions?
Answer and explanation
Correct answer: 9
A pair of linear equations has infinitely many solutions when the ratios of corresponding coefficients and constants are equal. Here, the second equation must be twice the first because 26=2×13 and 104=2×52. Therefore, 18=2q, giving q=9. Hence, option C is correct. Exam tip: For infinitely many solutions, verify a₁/a₂=b₁/b₂=c₁/c₂.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
A pair of linear equations has infinitely many solutions when the ratios of corresponding coefficients and constants are equal. Here, the second equation must be twice the first because 26=2×13 and 104=2×52. Therefore, 18=2q, giving q=9. Hence, option C is correct. Exam tip: For infinitely many solutions, verify 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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