What is the value of (b) for (5x+by=20) and (10x+6y=40) to have infinitely many solutions?
Answer and explanation
Correct answer: 3
For two linear equations to have infinitely many solutions, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) must hold. Here, \(\frac{5}{10}=\frac{20}{40}=\frac{1}{2}\), so \(\frac{b}{6}=\frac{1}{2}\), giving \(b=3\). If \(b=4\), then \(\frac{b}{6}\neq\frac{1}{2}\), so the equations would not have infinitely many solutions. Exam tip: For infinitely many solutions, verify that all three corresponding ratios are equal.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For two linear equations to have infinitely many solutions, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) must hold. Here, \(\frac{5}{10}=\frac{20}{40}=\frac{1}{2}\), so \(\frac{b}{6}=\frac{1}{2}\), giving \(b=3\). If \(b=4\), then \(\frac{b}{6}\neq\frac{1}{2}\), so the equations would not have infinitely many solutions. Exam tip: For infinitely many solutions, verify that all three corresponding ratios are equal.
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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