[tex]\left\{\begin{array}{ccc}-x+2y+z=10\\z=6\\3x-2y+2z=8\end{array}\right\\\\\text{Put the value of z to the first and the second equation:}\\\\\left\{\begin{array}{ccc}-x+2y+6\\3x-2y+2(6)=8\end{array}\right\\\\\left\{\begin{array}{ccc}-x+2y+6=10&|\text{subtract 6 from both sides}\\3x-2y+2(6)=8\end{array}\right\\\\\left\{\begin{array}{ccc}-x+2y=4\\3x-2y+12=8&|\text{subtract 12 from both sides}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x+2y=4\\3x-2y=-4\end{array}\right}\qquad\text{add both sides of the equations}[/tex]
[tex].\qquad2x=0\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=0}\\\\\text{Put the value of x to the first equation:}\\\\-0+2y=4\\2y=4\qquad\text{divide both sides by 2}\\\boxed{y=2}\\\\Answer:\ \boxed{x=0,\ y=2,\ z=6\to(0,\ 2,\ 6)}[/tex]
