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Thanks to kcrisman (http://ask.sagemath.org/question/347) I found a method using loops:

var('A,B')
f(x) = A*x + B
sol = solve([f(3) == 5, f(7) == -3], A, B)
for s in sol[0]:
    f = f.subs(s)
...

Now I can plot f, or use it to solve other equations. That's still a little cumbersome, when I have multiple equations to solve and substitutions to apply. If you have a loopless method, please post.