smypy not returning solution using solve

I’m attempting to calculate Lagrange multiplier using a question from this youtube video: https://www.youtube.com/watch?v=B0yzLgJ6wn8, however using sympy.solve does not return solutions

I’ve coded this in python

import sympy as sp

x, y = sp.var('x y')

# constraint
g1 = 2 * x + y - 100
# function
f = 2 * x + 2 * x * y + y

# lambda
g1L = sp.Symbol('g1L')

fin_eqs = []
for i in [x, y]:
    fin_eqs.append(
        sp.Eq(
            sp.simplify(f.diff(i)), 
            sp.simplify(
                g1.diff(i) * g1L
            )
        )
    )
fin_eqs.append(sp.Eq(sp.simplify(g1), 0))


for i in fin_eqs:
    print(i)
"""
prints
Eq(2*y + 2, 2*g1L)
Eq(2*x + 1, g1L)
Eq(2*x + y - 100, 0)
which I've confirmed is correct
"""


sp.solve(fin_eqs, x, y) # returns []

However, it does not work out that x = 25 and y = 50

>Solution :

For some reason, to get result you need to omit symbols you’re solving your system of equations on.

sp.solve(fin_eqs) returns {g1L: 51, x: 25, y: 50}