Find the value of (a) for infinitely many solutions of (8x+ay=12) and (20x+10y=30).
Answer and explanation
Correct answer: \(a=4\)
For infinitely many solutions, the two linear equations must represent the same line; hence \(\frac{8}{20}=\frac{a}{10}=\frac{12}{30}\). Here, \(\frac{8}{20}=\frac{12}{30}=\frac{2}{5}\). Therefore, \(\frac{a}{10}=\frac{2}{5}\), which gives \(a=4\). For \(a=3,5\), or \(6\), the ratios of the corresponding coefficients are not equal. Exam tip: for infinitely many solutions, check that \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\).
Frequently asked questions
What is the correct answer to this question?
\(a=4\)
Why is this the correct answer?
For infinitely many solutions, the two linear equations must represent the same line; hence \(\frac{8}{20}=\frac{a}{10}=\frac{12}{30}\). Here, \(\frac{8}{20}=\frac{12}{30}=\frac{2}{5}\). Therefore, \(\frac{a}{10}=\frac{2}{5}\), which gives \(a=4\). For \(a=3,5\), or \(6\), the ratios of the corresponding coefficients are not equal. Exam tip: for infinitely many solutions, check that \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\).
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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