I would use eliminateion
look at first equation and second
x+y+z=4 and
x+y-z=4
notice
x+y+z=4=x+y-z
or
x+y+z=x+y-z
minus (x+y) both sides
z=-z
therefor z=0 since that is the only number that works
sub 0 for all z
we now have
x+y=4 and
3x+3y=12
that doesn't help
infinitely many solutions for x and y and z=0
the solution is the line x+y=4 or y=-x+4 and z=0 (since z=0, the graph is on the xy plane)
