Question:
Find the value of k for which the system kx 2y = 5 and 3x y = 1 has (i) a unique solution and (ii) no solution
Answer:
Given equations are:
kx + 2y = 5
3x + y = 1
1. For unique solution:
k/3 ≠ 2/1
=> k/3 ≠ 2
=> k ≠ 2 * 3
=> k ≠ 6
2. For no solution:
k/3 = 2/1 ≠ 5/1
=> k/3 = 2 or k/3 ≠ 5
=> k = 2 * 3 or k ≠ 5 * 3
=> k = 6 or k ≠ 15
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