Solving 3 simultaneous equations It's been a while since I've had to do a simultaneous equation and I'm rusty on a few of the particulars. 
Say for example I have the following equations:
x + y       = 7
2x + y + 3z = 32
    2y + z  = 13

I know that I need to combine the above 3 equations into 2 other equations, for example, if I combine (counting down) 1 + 2 I'd get
3x + 2y + 3z = 32

And combing 2 with 3 I'd get 
2x + 3y + 4z = 45

Which is fine, and I understand. It's the next steps I have trouble understanding. A lot of the examples I've been looking at have a value for each of the x, y z. Looking at this site here I'm not sure what is going on step 2. 
I can see that they are multiplying one line by 2. Is that something you always do? Like, with simultaneous equations do you always multiple one of the equations by 2? If not, how do you determine which number to use? 
My understanding of simultaneous equations is extremely limited. 

You can "eliminate" one or more of the equations using one of the techniques already listed here. For systems of equations with three variables, a technique my intermediate calculus class uses to find critical points is to solve for one of the variables in (1), substitute that variable into (2) to solve for the unknown, and check validity by subbing both into (3).
