What is the correct solution status for (13x+2y=31) and (6x+y=14)?
Answer and explanation
Correct answer: One unique solution
For a pair of linear equations, the condition \(a_1/a_2 \ne b_1/b_2\) indicates a unique solution. Here, \(13/6 \ne 2/1\), so the two lines intersect at exactly one point. Therefore, the correct answer is one unique solution. Infinitely many solutions require the corresponding coefficient and constant ratios to be equal, while exactly two solutions are not possible for a pair of linear equations. Exam tip: first compare \(a_1/a_2\) and \(b_1/b_2\).
Frequently asked questions
What is the correct answer to this question?
One unique solution
Why is this the correct answer?
For a pair of linear equations, the condition \(a_1/a_2 \ne b_1/b_2\) indicates a unique solution. Here, \(13/6 \ne 2/1\), so the two lines intersect at exactly one point. Therefore, the correct answer is one unique solution. Infinitely many solutions require the corresponding coefficient and constant ratios to be equal, while exactly two solutions are not possible for a pair of linear equations. Exam tip: first compare \(a_1/a_2\) and \(b_1/b_2\).
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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