Question

Solve the system of linear equations and check any solution algebraically

Answer 1

It is pretty long, hope you understand 
  x+y+z=6
+
  2x-y+z=3
-------------
  3x+2z=9
->3x=9-2z (1)

3x-z=0
3x=z (2)

From (1)+(2)-> z=9-2z
solve for z
-3z=9
z=-3 (3)

plug (3) in (2)
->3x=-3
->x=-1 (4)

Plug (3) and (4) in x+y+z=6
-3+y+(-3)=6
solve for y
y-6=6
->y=12
Answer:
x=-1
y=12
z=-3

Answer 2

The answer to the problem is (1, 2, 3).