If a pair of linear equations is written as \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), under which condition will it have a unique solution?
Answer and explanation
Correct answer: \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\)
When \(a_1/a_2\ne b_1/b_2\), the two lines have different slopes and intersect at exactly one point, so the solution is unique. Option B represents parallel lines. Exam tip: compare the ratios of the \(a\) and \(b\) coefficients first.
Frequently asked questions
What is the correct answer to this question?
\(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\)
Why is this the correct answer?
When \(a_1/a_2\ne b_1/b_2\), the two lines have different slopes and intersect at exactly one point, so the solution is unique. Option B represents parallel lines. Exam tip: compare the ratios of the \(a\) and \(b\) coefficients first.
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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