CUET · MATHS · PYQ PAPER 2025
The system of equations \(2 x+\lambda y=8, \lambda x+8 y=3\) has a unique solution if the value of \(\lambda\) is (are):
- A \(\lambda \neq \pm 4\)
- B \(\lambda=4\)
- C \(\lambda=-4\)
- D \(\lambda\) is any real number
Answer & Solution
Correct Answer
(A) \(\lambda \neq \pm 4\)
Step-by-step Solution
Detailed explanation
For a unique solution, the determinant of the coefficient matrix must be non-zero: \(\begin{vmatrix} 2 & \lambda \\ \lambda & 8 \end{vmatrix} \neq 0\) \(2(8) - \lambda(\lambda) \neq 0\) \(16 - \lambda^2 \neq 0\) \(\lambda^2 \neq 16\) \(\lambda \neq \pm 4\)
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