I have found a couple of other online equation solvers that I like:
This one lays out the equations using high school algebra, but you need to enter coefficients of 0 for all the unused variables in each row. It can solve up to 10×10.
This one also lays out the equations using high school algebra, but can only solve up to 6×6. However, the zeros are already filled in.
This one allows you to enter the matrices as text, and will solve for you. I do not know how large of a matrix it will accept.
And this one will allow you to solve up to 9×9 matrices.