That would work, but it would be the best way.

First you should observe that z is already eliminated
from the third equation, so you should eliminate z 
from the first two equations:

To eliminate z from the first two equations:

Multiply the first equation by 3 and the second equation 
by 7, then add them:

3[-10x - 11y + 7z = 145]
7[  7x -  4y - 3z =  53]

  -30x - 33y + 21z = 435
   49x - 28y - 21z = 371
   19x - 61y       = 806

Now we take the third original equation with
this equation and solve this system:



We can do this by substitution:

Solve the first equation for y:



Substitute  for  in








Substitute that into 





Now substitute  and  into
either one of the first two original equations.








Edwin