Which condition gives a unique solution for ((s+2)x+3y=1) and (5x+(s-1)y=4)?
Answer and explanation
Correct answer: \(s^2+s-17\ne 0\)
A pair of linear equations has a unique solution when its coefficient determinant is non-zero. Here, \(D=(s+2)(s-1)-3\times5=s^2+s-17\). Therefore, the required condition is \(s^2+s-17\ne 0\). In option A, the determinant becomes zero, so a unique solution is not possible. Exam tip: use \(a_1b_2-a_2b_1\ne0\) to test for a unique solution.
Frequently asked questions
What is the correct answer to this question?
\(s^2+s-17\ne 0\)
Why is this the correct answer?
A pair of linear equations has a unique solution when its coefficient determinant is non-zero. Here, \(D=(s+2)(s-1)-3\times5=s^2+s-17\). Therefore, the required condition is \(s^2+s-17\ne 0\). In option A, the determinant becomes zero, so a unique solution is not possible. Exam tip: use \(a_1b_2-a_2b_1\ne0\) to test 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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