x - 2y +  z =  6.   (1)
2x +  y - 3z = -3,   (2)
 x - 3y + 3z = 10.   (3)

Let us apply the Gauss' elimination procedure. Multiply first eqn by 2 and then distract it from the second eqn. Then distract the first eqn from the third one. You will get

 x - 2y +  z =  6.   (4)
     5y - 5z = -15.  (5)
    -y  + 2z =  4.   (6)

Thus you excluded x in the eqns (5) and (6). Next, in the eqn (5) divide both sides by 5. You will get

 x - 2y +  z =  6.   (7)
      y -  z = -3 .  (8)
     -y + 2z =  4.   (9)

Now, add equations (8) and (9). You will get

 x - 2y +  z =  6.   (10)
      y -  z = -3 .  (11)
           z =  1.   (12)

So, you just found the solution z = 1. Now, make back substitution in equations (11) and (10) and find y and then x.