What value of (a) gives infinitely many solutions for (5x+ay=15) and (10x+6y=30)?
Answer and explanation
Correct answer: 3
For two linear equations to have infinitely many solutions, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Here, \(\frac{5}{10}=\frac{a}{6}=\frac{15}{30}=\frac{1}{2}\). Thus, \(\frac{a}{6}=\frac{1}{2}\), giving \(a=3\). Therefore, option B is correct. Exam tip: infinitely many solutions require all three corresponding ratios to be equal, not just two of them.
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, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Here, \(\frac{5}{10}=\frac{a}{6}=\frac{15}{30}=\frac{1}{2}\). Thus, \(\frac{a}{6}=\frac{1}{2}\), giving \(a=3\). Therefore, option B is correct. Exam tip: infinitely many solutions require all three corresponding ratios to be equal, not just two of them.
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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