Which condition gives a unique solution for (ax+7y=13) and (5x+by=9)?
Answer and explanation
Correct answer: \(ab\neq 35\)
For a pair of linear equations to have a unique solution, the determinant of the coefficient matrix must be non-zero. Here, \(D=ab-(7\times5)=ab-35\). Therefore, a unique solution exists when \(ab\neq 35\). If \(ab=35\), the determinant is zero, so the pair has either no solution or infinitely many solutions, not a unique solution. Exam tip: Check whether \(a_1b_2-a_2b_1\neq0\) for a unique solution.
Frequently asked questions
What is the correct answer to this question?
\(ab\neq 35\)
Why is this the correct answer?
For a pair of linear equations to have a unique solution, the determinant of the coefficient matrix must be non-zero. Here, \(D=ab-(7\times5)=ab-35\). Therefore, a unique solution exists when \(ab\neq 35\). If \(ab=35\), the determinant is zero, so the pair has either no solution or infinitely many solutions, not a unique solution. Exam tip: Check whether \(a_1b_2-a_2b_1\neq0\) for a unique solution.
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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