Algebraically solve the system of equations using any method you wish

Question

3x-10y+z=5
-4x+9y-z=-6
-13y+z=2

Answer 1

I would use substitution to start:
from the 3rd: z = 13y + 2

into the 1st:
3x - 10y + 13y + 2 = 5
3x + 3y = 3
x+y=1

into the 2nd:
-4x + 9y - 13y - 2 = -6
-4x - 4y = -4
x + y = 1

Ahhh,
x+y = 1 and x+y = 1 don't have a real solution.
So the system has no unique solution.

check my arithmetic