What is the value of (b) for (3x+by=24) and (12x+20y=96) to have infinitely many solutions?
Answer and explanation
Correct answer: 5
For two linear equations to have infinitely many solutions, the dependent-pair condition \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) must hold. Here, \(\frac{3}{12}=\frac{24}{96}=\frac{1}{4}\), so \(\frac{b}{20}=\frac{1}{4}\), giving \(b=5\). Therefore, option C is correct. Exam tip: for infinitely many solutions, all three corresponding ratios must be equal; equality of only two ratios is not sufficient.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
For two linear equations to have infinitely many solutions, the dependent-pair condition \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) must hold. Here, \(\frac{3}{12}=\frac{24}{96}=\frac{1}{4}\), so \(\frac{b}{20}=\frac{1}{4}\), giving \(b=5\). Therefore, option C is correct. Exam tip: for infinitely many solutions, all three corresponding ratios must be equal; equality of 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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