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The system of equations x + y + z = 6, x + 2y + 5z = 9, x + 5y + λz = μ, has no solution if

1. λ = 17, μ ≠ 18
2. λ ≠ 17, μ ≠ 18
3. λ = 15, μ ≠ 17
4. λ = 17, μ = 18

Correct answer: λ = 17, μ ≠ 18

Solution

The system has no solution when the third equation becomes inconsistent with the first two. When λ equals 17, the third equation's coefficients align with the first two, but if μ is not equal to 18, it creates a contradiction, leading to no possible solution.

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