When will (mx+7y=13) and (16x+14y=26) have a unique solution?
Answer and explanation
Correct answer: \(m\neq 8\)
A pair of linear equations has a unique solution when \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). Here, \(\frac{m}{16}\neq\frac{7}{14}=\frac12\) is required. Therefore, the pair has a unique solution for \(m\neq8\). If \(m=8\), then \(\frac{m}{16}=\frac{7}{14}=\frac{13}{26}=\frac12\), so both equations represent the same line and have infinitely many solutions. Exam tip: for a unique solution, the ratios of the corresponding coefficients must be unequal.
Frequently asked questions
What is the correct answer to this question?
\(m\neq 8\)
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, \(\frac{m}{16}\neq\frac{7}{14}=\frac12\) is required. Therefore, the pair has a unique solution for \(m\neq8\). If \(m=8\), then \(\frac{m}{16}=\frac{7}{14}=\frac{13}{26}=\frac12\), so both equations represent the same line and have infinitely many solutions. Exam tip: for a unique solution, the ratios of the corresponding coefficients must be unequal.
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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