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Show that the system of equations 3x - y + 4z = 3, x + 2y - 3z = -2 and 6x + 5y + λz = - 3

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Show that the system of equations 3x - y + 4z = 3, x + 2y - 3z = -2 and 6x + 5y + λz = - 3 has at least one solution for any real number λ ≠ - 5. Find the set of solutions, if λ = - 5

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The given system of equations 

3x - y + 4z = 3, 

x + 2y - 3z = - 2, 

6x + 5y + λz = - 3 has at least one solution. if Δ ≠ 0

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