If the graphs of the two linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) are coincident lines, which condition correctly shows that they have infinitely many solutions?
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 every point on that line satisfies both equations and gives infinitely many solutions. Hence all three coefficient ratios must be equal. In option B, the lines are parallel but distinct. Exam tip: for infinitely many solutions, check equality of 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?
Coincident lines represent the same line, so every point on that line satisfies both equations and gives infinitely many solutions. Hence all three coefficient ratios must be equal. In option B, the lines are parallel but distinct. Exam tip: for infinitely many solutions, check equality of 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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