The system of equations

x + y + z = 6;

x + 4y + 6z = 20;

x + 4y + λz = μ

has NO solution for values of λ and μ given by

1
λ = 6, μ = 20
2
λ = 6, μ ≠ 20
3
λ ≠ 6, μ = 20
4
λ ≠ 6, μ ≠ 20

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