Question 33856
<pre><b><font size = 4> x + 3y - 6z = 7   
2x -  y +  z = 1 
 x + 2y + 2z = 1

1.  Use the 1st equation to eliminate x from the 2nd equation.

2.  Use the 1st equation to eliminate x from the 3rd equation.

3.  Use the 2nd equation to eliminate y from the 3rd equation.

4.  Solve the 3rd equation for z.

5.  Substitute the value of z in the 2nd equation to find y.

6. Substitute the values of y and z in the 1st equation to solve 
   for x.

 x + 3y - 6z = 7  
2x -  y +  z = 1 
 x + 2y + 2z = 1

Get rid of the 2x by adding -2 times the 1st equation to 
1 times the 2nd:

-2[ x + 3y - 6z = 7]  
 1[2x -  y +  z = 1] 
    x + 2y + 2z = 1

 x + 3y -  6z =   7  
    -7y + 13z = -13
 x + 2y +  2z =   1

Get rid of the x on the bottom left by adding -1 times the 
1st equation to 1 times the 3rd:

 -1[x + 3y -  6z =   7   
       -7y + 13z = -13
  1[x + 2y +  2z =   1

 x + 3y -  6z =   7   
    -7y + 13z = -13
     -y +  8z =  -6

Get rid of the -y on the by adding -1 times the 
2nd equation to 7 times the 3rd:

    x + 3y -  6z =   7   
-1[    -7y + 13z = -13
 7[    -y +  8z =  -6

 x + 3y -  6z =   7   
    -7y + 13z = -13
          43z = -29

Solve the bottom equation for z and get z = -29/43

Replace z by -29/43 in the second equation

-7y + 13(-29/43) = -13
Clear of fractions by multiplying by 43

-301y - 377 = -559

-301y = -182
    y = -182/(-301) = 26/43

Replace y by 26/43 and z by -29/43 in the 1st equation:

       x + 3y -  6z =   7
        x +  3(26/43) - 6(-29/43) = 7

Clear of fractions by multiplying through by 43

         43x + 78 + 174 = 301
              43x + 252 = 301
                    43x =  49    
                      x = 49/43


So x = 49/43, y = 26/43, z = -29/43
Edwin
AnlytcPhil@aol.com</pre>