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प्रश्न
Find the value of k for which the following system of equations has a unique solution:
kx + 2y = 5
3x + y = 1
बेरीज
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उत्तर
Given: kx + 2y = 5, 3x + y = 1
Form the coefficient matrix and its determinant:
D = `|(k, 2), (3, 1)|`
= k × 1 – 2 × 3
= k – 6
A 2 × 2 linear system has a unique solution if its determinant ≠ 0, so k – 6 ≠ 0 ⇒ k ≠ 6.
The system has a unique solution for all real k except k = 6.
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