Solve the following system of equations:

-x + 5y - 2z =  2
-x + 4y + 5z =  1
 x - 6y + 4z = -3

1. Pick any pair of equations and eliminate any letter.
2. Pick ANOTHER pair of equations and eliminate the SAME letter 
   you eliminated in step 1.
3. Solve the resulting system of 2 equations and 2 unknowns
4. Substitute the values found in step 3 in any of the original
   equations to find the 3rd letter, the one eliminated in step 1.

1. Pick equations 2 and 3 and pick x to eliminate.  All we need do
   is add them term by term:


-x + 4y + 5z =  1
 x - 6y + 4z = -3
—————————————————
    -2y + 9z = -2

2. Pick equations 1 and 3 and eliminate x.  All we need do
   is add them term by term:  
  
-x + 5y - 2z =  2
 x - 6y + 4z = -3
—————————————————
     -y + 2z = -1

3.  Solve the system

    -2y + 9z = -2
     -y + 2z = -1

You should already know how to solve this. If not post again.

Answer to this part: y = 1, z = 0

4.  Pick the third original equation

         x - 6y + 4z = -3
     x - 6(1) + 4(0) = -3
           x - 6 + 0 = -3
               x - 6 = -3
                   x = 3

Final solution (x, y, z) = (3, 1, 0)

Edwin
AnlytcPhil@aol.com