When will (ex-4y=9) and (18x-12y=27) have a unique solution?
Answer and explanation
Correct answer: \(e\ne 6\)
A pair of linear equations has a unique solution when the ratios of the coefficients are unequal. Here, \(\frac{e}{18}\ne\frac{-4}{-12}=\frac13\), which gives \(e\ne6\). If \(e=6\), all three ratios become \(\frac13\), so the pair has infinitely many solutions rather than a unique solution. Exam tip: for a unique solution, check \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\).
Frequently asked questions
What is the correct answer to this question?
\(e\ne 6\)
Why is this the correct answer?
A pair of linear equations has a unique solution when the ratios of the coefficients are unequal. Here, \(\frac{e}{18}\ne\frac{-4}{-12}=\frac13\), which gives \(e\ne6\). If \(e=6\), all three ratios become \(\frac13\), so the pair has infinitely many solutions rather than a unique solution. Exam tip: for a unique solution, check \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\).
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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