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If the system of linear equations x + ay + z = 3, x + 2y + 2z = 0, x + 5y + 3z = b has no solution, then
- (A) a = 1, b ≠ 9
- (B) a ≠ −1, b = 9
- (C) a = −1, b = 9
- (D) a = −1, b ≠ 9
Correct answer: (D) a = −1, b ≠ 9
Solution
For the system to have no solution, the equations must be inconsistent. Setting a = -1 leads to a situation where the first equation becomes dependent on the others, while b must not equal 9 to ensure that the third equation does not align with the others, thus creating inconsistency.
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