When will the pair (kx+5y=10) and (6x+15y=18) have a unique solution?
Answer and explanation
Correct answer: \(k\neq2\)
A pair of linear equations \(a_1x+b_1y=c_1\) and \(a_2x+b_2y=c_2\) has a unique solution when \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). Here, \(\frac{k}{6}\neq\frac{5}{15}=\frac{1}{3}\), which gives \(k\neq2\). At \(k=2\), the ratios of the coefficients on the left-hand sides are equal, so the solution cannot be unique. Exam tip: for a unique solution, compare the ratios of the coefficients of \(x\) and \(y\).
Frequently asked questions
What is the correct answer to this question?
\(k\neq2\)
Why is this the correct answer?
A pair of linear equations \(a_1x+b_1y=c_1\) and \(a_2x+b_2y=c_2\) has a unique solution when \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). Here, \(\frac{k}{6}\neq\frac{5}{15}=\frac{1}{3}\), which gives \(k\neq2\). At \(k=2\), the ratios of the coefficients on the left-hand sides are equal, so the solution cannot be unique. Exam tip: for a unique solution, compare the ratios of the coefficients of \(x\) and \(y\).
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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