What will be the value of (a) for (4x+ay=36) and (12x+21y=108) to have infinitely many solutions?
Answer and explanation
Correct answer: 7
For two linear equations to have infinitely many solutions, the ratios of the corresponding coefficients and constants must be equal: 4/12 = a/21 = 36/108. Since 4/12 and 36/108 are both 1/3, we get a/21 = 1/3, so a = 7. Therefore, option C is correct. Exam tip: For infinitely many solutions, all three corresponding ratios must be equal; checking only two ratios is not sufficient.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For two linear equations to have infinitely many solutions, the ratios of the corresponding coefficients and constants must be equal: 4/12 = a/21 = 36/108. Since 4/12 and 36/108 are both 1/3, we get a/21 = 1/3, so a = 7. Therefore, option C is correct. Exam tip: For infinitely many solutions, all three corresponding ratios must be equal; checking only two ratios is not sufficient.
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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