Solving 3 Equations with 3 Unknowns (using gauss method)

Question

x-y-z=1

x+3y+3z=-1

x+y+z=0

Answer 1

using your TI-83 calculator, press end-matrix-edit and enter the following 4x4 matrix

(1,1,-1,1),(1,3,3,-1),(1,1,1,0),(0,0,0,0)

next press 2nd-quit to save

next press 2nd-matrix-math-rref(

enter

rref(a) on home panel , enter

(1,0,0,1/2),(0,1,0,0),(0,0,1,-1/2)

back filling the rows

x=1/2, y=0,z=-1/2

Answer 2

Looking at equations, I don't think you can obtain a unique solution.  Add the first and third equation:

x - y - z = 1

x + y + z = 0
-----------------------
2x + 0 + 0 = 1

x = 1/2  since the y and z variables cancelled
  
Therefore, your solution would be:

 

x = 1/2  and z = f(y)

 

I can solve this but it not by gaussian elimination which is what you are trying to do. Sorry!