A command-line utility to solve a system of linear equations
List comprehensions

List comprehensions are a cool feature that could shorten your code, at many places.
For example instead of this:


    values = []
    for item in X:
        values.append(Fraction(item[0, 0]).limit_denominator())



You can write like this:

    values = [Fraction(item[0, 0]).limit_denominator() for item in X]


Another example:


    vars = []
    for i in range(0, len):
        vars.append(raw_input())



Better this way:

    vars = [raw_input() for _ in range(len)]


There are some more tips in there:


range(len) is equivalent to range(0, len)
When you don't use the loop variable in the loop body, the convention is to name the loop variable _


There are other places in your code that you could shorten using list comprehensions, I suggest to rewrite them all.

Magic values

The number 23 is a magic value here:    


    # x is the 24th alphabet
    start = 23 if len &lt;= 3 else 0



Although the comment explains it, it would be better to put the value in a constant with a name that describes its purpose.
And instead of the hard-coded number, I suggest to express it in a programmatic way, for example:

POS_X = ord('x') - ord('a')


When written this way, we don't even have to know what the value really is (23), the important thing is its relative position from the letter 'a'.

Code duplication

The solve calls are duplicated here, except for the 3rd parameter:


    if varlist is None:
        answer = solve(A, B, vars(rows))
    else:
        answer = solve(A, B, list(varlist))
    print_answer(answer)



It would be better to reorganize the code to eliminate such duplication:

    if varlist is None:
        varlist = vars(rows)

    answer = solve(A, B, varlist)
    print_answer(answer)


Of course, in your current implementation varlist is not really a list.
It would be better to fix that, and make it a list when you assign it earlier, for example:

elif num == 4:
    script, a, symbols, b = argv
    varlist = list(symbols)