there are several handy calculators for this. You can see the details at
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
use gauss jordan elimination method tofind solution set of4x+5y+3z=23.3x+2y+z=10.2x+5y-z=9
2 answers
x=3/2,y=4,z=1/5