Determine the set of integer solutions of the system:

3x + y + 2z -t =1 (mod 5)

2x + y + 4z +3t +2w=1 (mod 5)

x - 2y +3t +w=3 (mod 5)

x -z -t +3w=1 (mod 5)

2x + 3y +3z - t -w=1(mod 5)

in which (mod 5) denotes congruence

modulo 5.

I would like to get some help in understanding the answer:"Treat the system as a system of equationsIs there no "direct solution" for

in which all calculations are done modulo 5. For example, adding the first row

to the second gives [0 2 1 2 2 2 ] "

finding x, y, z ,t,w?

Thanks in advance for any help you are able to provide...