Which condition indicates that a pair of linear equations in two variables has infinitely many solutions?
Answer and explanation
Correct answer: \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
When \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), both equations represent the same line, so infinitely many common points exist. Option B represents distinct parallel lines. Exam tip: compare all three ratios.
Frequently asked questions
What is the correct answer to this question?
\(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
Why is this the correct answer?
When \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), both equations represent the same line, so infinitely many common points exist. Option B represents distinct parallel lines. Exam tip: compare all three ratios.
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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