Solving matrices is pretty easy, but augmented matrices. i.e
[1 2 3:4]
[3 4 5:6]
[1 0 4:7]
You have to get it to look like the identity matrix
[1 0 0: x]
[0 1 0:y]
[0 0 1:z]
by doing certain operations, and I don't think you can do it on a calculator in less than a minute.