Solve the system analytically: 

 x +  y +  z = 10
2x + 6y + 2z = 40
-x + 7y - 3z = 26


1.  Pick two equation and a letter to eliminate

I will pick equations 1 and 3 and x to eliminate

 x +  y +  z = 10
-x + 7y - 3z = 26

If you just add them as they are, the x's will be
eliminated:

 x +  y +  z = 10
-x + 7y - 3z = 26
-----------------
     8y - 2z = 36

2.  Pick a different pair of equation and the SAME
    letter to eliminate.  (You must pick one equation
    the same as before but pick the other of them 
    different 

I will pick equations 1 and 2 and eliminate x

 x +  y +  z = 10
2x + 6y + 2z = 40

If you multiply the first through by -2, the x's 
will be eliminated when you add them:

-2x - 2y - 2z = -20
 2x + 6y + 2z =  40
-------------------
      4y      =  20
            y =   5 

3.  Solve the system:

     
     8y - 2z = 36
           y =  5

Substitute:

   8(5) - 2z = 36
     40 - 2z = 36
         -2z = -4
           z = 2

Substitute y = 5 and z = 2 in the
first original equation:

      x + y + z = 10
      x + 2 + 5 = 10
          x + 7 = 10
              x = 3

So the solution is (x,y,z) = (3,5,2)

Edwin
 

            

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