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 eqution 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.
Step 1. One of the equations has only two unknowns, in fact two of them
do. I'll pick the first one 
and call it "equation 1"
I observe that the unknown x is missing from "equation 1" and
so I'll eliminate x from the other two equations:
To eliminate the x's we multiply one of them, say the first, by -1
to make the x's cancel when I add them term by term:
Result:
, that's "equation 2".
Now we solve the system consisting of equation 1 and equation 2:
Swap the two terms on the left of the first one so the unknowns
will be in the same order:
To make the z's cancel when we add them term by term, we multiply the
first one through by -1:
Result:
Substitute that in
Substitute those in the original equation
Solution: 
Edwin
