I would use substitution to start:
from the 3rd: z = 13y + 2
into the 1st:
3x - 10y + 13y + 2 = 5
3x + 3y = 3
into the 2nd:
-4x + 9y - 13y - 2 = -6
-4x - 4y = -4
x + y = 1
x+y = 1 and x+y = 1 don't have a real solution.
So the system has no unique solution.
check my arithmetic
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