Which condition gives a unique solution for ((y+1)x+2y=3) and (5x+(y-2)y=4)?
Answer and explanation
Correct answer: \(y^2-y-12\neq0\)
Under the intended interpretation that \(y\) is a parameter appearing in the coefficients, the coefficient determinant is \(D=a_1b_2-a_2b_1=(y+1)(y-2)-2\times5=y^2-y-12\). A pair has a unique solution exactly when \(D\neq0\); hence \(y^2-y-12\neq0\) is correct. In option A, \(D=0\), so the solution cannot be unique. Exam tip: test \(a_1b_2-a_2b_1\neq0\) for a unique solution.
Frequently asked questions
What is the correct answer to this question?
\(y^2-y-12\neq0\)
Why is this the correct answer?
Under the intended interpretation that \(y\) is a parameter appearing in the coefficients, the coefficient determinant is \(D=a_1b_2-a_2b_1=(y+1)(y-2)-2\times5=y^2-y-12\). A pair has a unique solution exactly when \(D\neq0\); hence \(y^2-y-12\neq0\) is correct. In option A, \(D=0\), so the solution cannot be unique. Exam tip: test \(a_1b_2-a_2b_1\neq0\) 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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