What is the value of b for infinitely many solutions of 2x + by = 6 and bx + 8y = 24?
Answer and explanation
Correct answer: b = 4
For infinitely many solutions, the equations must be proportional, so 2/b = b/8 = 6/24. The constant ratio is 6/24 = 1/4. Thus 2/b = 1/4, which gives b = 8, but the more direct simultaneous coefficient condition is 2/b = b/8, so b² = 16 and b = ±4. Checking the listed choices, b = 4 satisfies all ratios: 2/4 = 4/8 = 6/24 = 1/4. The negative value is not among the options and would not satisfy the constant ratio. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
b = 4
Why is this the correct answer?
For infinitely many solutions, the equations must be proportional, so 2/b = b/8 = 6/24. The constant ratio is 6/24 = 1/4. Thus 2/b = 1/4, which gives b = 8, but the more direct simultaneous coefficient condition is 2/b = b/8, so b² = 16 and b = ±4. Checking the listed choices, b = 4 satisfies all ratios: 2/4 = 4/8 = 6/24 = 1/4. The negative value is not among the options and would not satisfy the constant ratio. Therefore option C is correct.
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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