Question

how do you solve linear systems with three variables??

Answer 1

similar to your systems with two variables, just a few more steps.
do you have a system with which I can demonstrate?

Answer 2

not actually

Answer 3

but can you give me one??

Answer 4

Several means exist. I like using matrices, but I suspect that you are not interested in reduced row echelon form. However, feel free to look that up later.

Try substitution with
x+y+z = 1
x + y -z = 0
x-y+z = 2

Answer 5

Well, you have three equations (you should) and three variables (x, y, z)
So what you do is you take one of them equations, and isolate one variable
That is to say, for instance

Using the first equation, express z in terms of x and y only.

Then substitute this new expression for z for the z's in the two other equations.

You'll end up with two equations and just x's and y's, and you proceed as if it's a system of two variables

Answer 6

http://www.mathwarehouse.com/algebra/planes/systems/three-variable-equations.php

Answer 7

thank you, all of you