When will (wx-6y=4) and (16x-24y=12) have a unique solution?
Answer and explanation
Correct answer: \(w\ne4\)
A pair of linear equations has a unique solution when the determinant of its coefficient matrix is non-zero. Here, the determinant is \(w(-24)-16(-6)=96-24w=24(4-w)\). It is non-zero when \(w\ne4\). At \(w=4\), the coefficients of \(x\) and \(y\) are in the same ratio, but the constants are not, so the lines are parallel and there is no solution. Exam tip: for a unique solution, check that \(a_1b_2-a_2b_1\ne0\).
Frequently asked questions
What is the correct answer to this question?
\(w\ne4\)
Why is this the correct answer?
A pair of linear equations has a unique solution when the determinant of its coefficient matrix is non-zero. Here, the determinant is \(w(-24)-16(-6)=96-24w=24(4-w)\). It is non-zero when \(w\ne4\). At \(w=4\), the coefficients of \(x\) and \(y\) are in the same ratio, but the constants are not, so the lines are parallel and there is no solution. Exam tip: for a unique solution, check that \(a_1b_2-a_2b_1\ne0\).
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
