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How to use python to solve the system of nonlinear equations like this? I will be very appreciative of your help!

{4 x^(-1/3) y^(1/3) - 8/3 x^(5/3) y^(1/3) + 10/3 x^(2/3) y^(4/3) - 2/3 (x^(-1/3) y^(7/3)) - 4/3 x^(1/3) y^(2/3) = x, 2 x^(2/3) y^(-2/3) - 1/3 x^(8/3) y^(-2/3) + 8/3 x^(5/3) y^(1/3) - 7/3 x^(2/3) y^(4/3) - 2/3 x^(4/3) y^(-1/3) = 2 y}

Litong Zhang
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    What did you try? Could you write your equations in Python notation? Could you explain what kind of solution you are expecting? Note that Python uses `**` powers and `*` for multiplication. – JohanC Apr 08 '22 at 10:27
  • First of all, be very careful when using `^` to mean "exponent" while writing python code. Python uses `**` for exponents, not `^`. Symbol `^` also exists in python, but it means something completely unrelated (bitwise xor), so your code won't produce an error message if you use `^` instead of `**`, but it will still be completely wrong. – Stef Apr 08 '22 at 12:23
  • Second, I suggest doing a change in variables. Let `X = x**(1/3)` and `Y = y**(1/3)`. Then rewrite your equation in terms of X and Y. All the **(1/3) will be gone, it will be a lot easier to see clearly. – Stef Apr 08 '22 at 12:23
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    Related: [How to solve a pair of nonlinear equations using Python?](https://stackoverflow.com/questions/8739227/how-to-solve-a-pair-of-nonlinear-equations-using-python) – Stef Apr 08 '22 at 12:25

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