Systems of equations

I know this is too easy for Anon and you will call me stupid. But I need help learning how to solve a system of 3 equations with 3 unknown variables. I have a problem here I need solved, but I really want to learn how to do it, and not just the answer. I was sick on the day they taught this and now I need to catch up. I hope you guys can help. Here is the problem I am on.

Solve the system:
X + Y + Z = 4
X - 2y - z = 1
2X - y - 2z = -1

If you can help to walk me through this I would be very grateful. Thanks

1) pick any two equations.
2) for each of those two equations, eliminate one of the three variables.  One of the ways to do that is to rearrange each equation to isolate the variable that is to be eliminated, then create a new equation by showing that each of the two equation's other sides are equal to each other.  Another method is the addition/subtraction of equations method.
3) repeat steps 1 and 2 but with a different pair of equations, being sure to eliminate the same variable that you chose to eliminate with the first pair.
4) you now have two new equations, each with only two variables.  You know how to solve for those two variables, I presume.
5) take your solutions from step 4 and pick any of the original three equations to substitute those solutions into, allowing you to solve for the third unknown variable.

Use matrices. (Yes I'm being a dick, but this is how you'll solve them once you get out of algebra.)

A= [1 1 1;
1 -2 -1;
2 -1 -2]

B= [X;
Y;
Z]

C=[4;
1;
-1]

A*B=C

ITT: NERDS

lol