x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
let's get rid of all the y's.
add these two equations...
x + y + z = -5
+ x - y + 3z = -1
--------------------------
2x + 4z = -6
2x = -6 - 4z
x = -2z -3
then add the last two equations..
x - y + 3z = -1
+ 4x + y + z = -2
5x + 4z = -3
4z = -5x -3
z = -5/4 - 3/4
substitute x = -2z -3 to any of the equations
-2z - 3 + y + z = -5
-z - 3 + y = -5
y = -2 + z
