[tex]\left\{\begin{array}{ccc}x-y+2z=7&(1)\\2x+y+z=8&(2)\\x-z=5&(3)\end{array}\right\\\\(3)\qquad x-z=5\qquad\text{add z to both sides}\\.\qquad x=5+z\\\\\text{Substitute it to (1) and (2):}\\\\\left\{\begin{array}{ccc}(5+z)-y+2z=7\\2(5+z)+y+z=8\end{array}\right\\\\\left\{\begin{array}{ccc}5+z-y+2z=7&\text{subtract 5 from both sides}\\10+2z+y+z=8&\text{subtract 10 from both sides}\end{array}\right[/tex]
[tex]\underline{+\left\{\begin{array}{ccc}3z-y=2\\3z+y=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad6z=0\qquad\text{divide both sides by 6}\\.\qquad\boxed{z=0}\\\\\text{Put the value of z to the second equation and to (3)}\\\\3(0)+y=-2\to\boxed{y=-2}\\\\x=5+0\to\boxed{x=5}\\\\Answer:\ \boxed{x=5,\ y=-2,\ z=0\to(5,\ -2,\ 0)}\to\boxed{C}[/tex]
