(x, y, z) =

The system is inconsistent because if you add to the third equation the second one and the first one multiplied by -2, then you get

x(2 + 0 - 2) + y(1 + 1 - 2) + z(5 +(-3) - 2) = -13 + 10 - 2(-1)

or 0 = -1.

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