What is the value of (t) for infinitely many solutions of (tx+9y=6) and (20x+15y=10)?
Answer and explanation
Correct answer: \(t=12\)
For infinitely many solutions, the two linear equations must represent the same line. Hence, the ratios of corresponding coefficients and constants must be equal: \(\frac{t}{20}=\frac{9}{15}=\frac{6}{10}\). Since \(\frac{9}{15}=\frac{6}{10}=\frac{3}{5}\), we get \(\frac{t}{20}=\frac{3}{5}\). Therefore, \(t=12\). For \(t=10\), \(\frac{t}{20}=\frac{1}{2}\), which is not equal to \(\frac{3}{5}\). Exam tip: use \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) to check for infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
\(t=12\)
Why is this the correct answer?
For infinitely many solutions, the two linear equations must represent the same line. Hence, the ratios of corresponding coefficients and constants must be equal: \(\frac{t}{20}=\frac{9}{15}=\frac{6}{10}\). Since \(\frac{9}{15}=\frac{6}{10}=\frac{3}{5}\), we get \(\frac{t}{20}=\frac{3}{5}\). Therefore, \(t=12\). For \(t=10\), \(\frac{t}{20}=\frac{1}{2}\), which is not equal to \(\frac{3}{5}\). Exam tip: use \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) to check for infinitely many solutions.
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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