Solve the system of equations. If the system has no solution, say it is inconsistent. (1) x + y + z = 3,(2) x - z = 1,(3) y - z = -4

Adding (1) and (2) leads to
(x+y+z)+(x-z)=3+1
2x+y=4
(4) y=4-2x

Adding (1) and (3) leads to
(x+y+z)+(y-z)=3-4
x+2y=-1

Replacing y with (4) leads to the solution for x:
x+2(4-2x)=-1
x+8-4x=-1
-3x=-9
x=3

Using x we can find y:
y=4-2x=4-2(3)=4-6=-2
y=-2 

Next we find z:
x+y+z=3
3-2+z=3
-2+z=0
z=2 

solution: (3, -2, 2)