When will (rx+5y=2) and (8x+10y=4) have a unique solution?
Answer and explanation
Correct answer: \(r\neq 4\)
A pair of linear equations has a unique solution when \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). Here, \(\frac{r}{8}\neq\frac{5}{10}=\frac12\), which gives \(r\neq4\). If \(r=4\), the two equations become proportional and have infinitely many solutions, not a unique solution. Exam tip: compare the ratios of the coefficients of \(x\) and \(y\) first.
Frequently asked questions
What is the correct answer to this question?
\(r\neq 4\)
Why is this the correct answer?
A pair of linear equations has a unique solution when \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). Here, \(\frac{r}{8}\neq\frac{5}{10}=\frac12\), which gives \(r\neq4\). If \(r=4\), the two equations become proportional and have infinitely many solutions, not a unique solution. Exam tip: compare the ratios of the coefficients of \(x\) and \(y\) 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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