In this system of equations, the value of variable z is known. So to get the values of the variables substitute z=2 to one of the equations. It is better if it is plug-in to the second equation since it composed of two variables only.
y + z=12
Then, solve for y.
Now that the values of y and z are known, solve for x. Plug-in them to the first equation.
`2x+y-3z = 10`
Therefore, the solution is (3,10,2).