Find x, y, and z.


Pick any letter and a pair of equations to eliminate that letter
from:

I pick the letter y, and the 1st and 2nd equations to eliminate
y from.



To eliminate y, we multiply the second equation through by 2
and add them term by term:





Now pick a DIFFERENT pair of equations and eliminate
the SAME letter, y, from them. I'll pick the 2nd and
3rd equations.  (You have to choose one of them the
same as before, but be sure to pick the other one as
the equation you have not yet used:



To eliminate y, we multiply the upper equation through
by 5 and the lower equation through by 2, and add them 
term by term:





Notice that this equation can be divided through by 3.
It isn't necessary to do this but if we do the numbers
will be smaller.  So I will divide it through by 3:



Now we take these two equations and now we have two
equations with two unknowns:



To eliminate z, multiply the first equation by -11,
and the second equation through by +8:



Add them term by term:





Substitute that into



Now go back and pick any of the
original equations which contains
y, and substitute these value for
x and z:

Picking the first original equation:



Solution:



Edwin