Rules for solving a system of three equations in three unknowns:

1. If one of the equations has only two unknowns, call it "equation 1".
Observe which of the three unknowns is missing from that equation and 
eliminate that unknown from the other two equations, and call the 
resulting equation "equation 2".

2. If all three equations contain all three unknowns, pick two of the 
three equations and eliminate an unknown from them, and call the 
resulting equation "equation 1".  Us the equation you haven't yet used with 
one of the others and eliminate that same letter.  Call the resulting 
equation "equation 2".

3. Solve the system of two equation in two unknowns, consisting of "equation
1" and "equation 2".

4. Find the third unknown by substituting in one of the original equations 
that contains that third unknown.



None of the equations have only two unknowns, so step 1 is out.  So we go 
to step 2.

I'll pick the first two equations and eliminate z, since all I have to is 
add them term by term and the z's will cancel:




Result:

, that's equation 1.

Now I'll pick the second one and the third one and eliminate that same 
variable z.  All I have to do is add them term by term and the z's will 
cancel:




  Result:

, that's equation 2.

Step 3 is to solve equation 1 and equation 2:



 All I have to do is add them term by term and the y's will
cancel:

The result is:




Substitute in







Step 4 is to substitute theose two values in one of the original 
equations to find the third letter z. I'll pick the first original 
equation:






solution 

Edwin