SymPy

Linear on [0..1]

from sympy import *

y1, y2, a, b = symbols('y1 y2 a b')

jscode(solve([
    c - y1,
    a + b - y3,
    ], (a, b)))
    

Cubic on [0..1]

from sympy import *

y1, y2, y3, y4, a, b, c, d = symbols('y1 y2 y3 y4 a b c d')

jscode(solve([
    d - y1,
    a * 1/3**3 + b * 1/3**2 + c * 1/3 + d - y2,
    a * 2**3/3**3 + b * 2**2/3**2 + c * 2/3 + d - y3,
    a + b + c + d - y4,
    ], (a, b, c, d)))
    

There is SymPy online: https://live.sympy.org