solve and express your answer in coordinate x,y,z
x+y+z=6
2x-y-z=-3
x-2y+3z=6
add #1 and #2 ----> 3x = 3
x=1
triple the 2nd
6x - 3y - 3z = -9
x-2y + 3z = 6
add them
7x - 5y = -3
but x=1
7 - 5y = -3
-5y = -10
y = 2
sub into the #1
x+y+z=6
1+2+z = 6
z = 3
(x,y,z) = (1,2,3)