Software to solve system of linear equations in non-standard form

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Is there software to use to solve more than 4 simultaneous linear equations? Wolfram Alpha is nice but it can only do up to 4? Wolfram Alpha is nice because it can handle a non-standard form, but limited to 4 equations.

Most software only seems to handle standard form like so:

Ax = b

My equations look like so:

P=0.4
s0 = (1-P)*s1
s1 = (1-P)*s2 + P*s0
s2 = (1-P)*s3 + P*s1
s3 = (1-P)*s4 + P*s2
s4 = P*s3

It's annoying at best to try to format them into an Ax=b form. Internally software implementations probably convert it to matrix form, but it would be nice to just feed it what I have.