If the graphs of two linear equations are coincident lines, which condition on the ratios of their coefficients is correct?
Answer and explanation
Correct answer: \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
Coincident lines represent the same line, so all corresponding coefficients must be in the same ratio: \(a_1/a_2=b_1/b_2=c_1/c_2\). Hence, there are infinitely many solutions. Exam tip: if only the first two ratios are equal and the third differs, the pair has no solution.
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?
Coincident lines represent the same line, so all corresponding coefficients must be in the same ratio: \(a_1/a_2=b_1/b_2=c_1/c_2\). Hence, there are infinitely many solutions. Exam tip: if only the first two ratios are equal and the third differs, the pair has no solution.
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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