Question 183507
This site shows how to do, and it solves it for you.

http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=sys
--------------------------
This works well, gives the answers so you can check your work.  You can write a computer program to do these (I did it years ago in Fortran), but I would use Excel and determinants to do it now.  I have an Excel sheet that does up to 4th order.