SOLUTION: write the system as a matirx x-3y+2z=-21 y-2z=12 z=2 solve the system by gauss- jordan elimintaion

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x-3y+2z=-21
   y-2z=12
      z=2 

Convert to matrix form:

 1  	 -3  	 2  	 -21 
 0  	 1  	 -2  	 12 
 0  	 0  	 1  	 2 

Now add 2 times the 3rd row to the 2nd row (and replace the second row with this result)

 1  	 -3  	 2  	 -21 
 0  	 1  	 0  	 16 
 0  	 0  	 1  	 2 

Then add -2 times the 3rd row to the 1st row (and replace the first row with this result)

 1  	 -3  	 0  	 -25 
 0  	 1  	 0  	 16 
 0  	 0  	 1  	 2 

Finally, add 3 times the 2nd row to the 1st row (and replace the first row with this result)

 1  	 0  	 0  	 23 
 0  	 1  	 0  	 16 
 0  	 0  	 1  	 2 

The right hand column represents the solutions. So the solutions are x = 23, y = 16 and z = 2