Solve the following system of equations.

x + y – 4z = –7
2x + 3y – 3z = –6
2x + 2y – z = 0

- subtract 3rd from second
 
2x +3y -3z = -6
2x +2y -z = 0

 0 y -2z = -6
 
- multiply first by -2 and assum by second
 
-2x -2y +8z = 14
  2x +3y -3z = -6

  0 y +5z = 8
 
y-2z=-6
y+5z=8
subtract second from first
 0 -7z =-14
z=2
 
y+5z=8
y+5*2=8
y+10=8
y=-2
 
z=2
y=-2
 
x+y -4z=-7
x +(-2) -4(2) = -7
x-2-8=-7 x-10=-7
x=3
 
x=3
y=-2
z=2