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I tried plugging these cubic and quadratic equations into Wolfram Alpha and Symbolab but both said the same thing, too much computing time required. Now I am struggling to solve these equations and I need help on a method to somehow manage to solve them without the brute force method of elimination or substitution. Do I need to possibly simplify them down more? Thanks in advance!

[The system of equations][1]

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    $\begingroup$ You miss the proper tag quartics . it is very simple to eliminate all variables but $\beta$ (done by hand). $\endgroup$
    – Claude Leibovici
    Commented Jun 11 at 5:57
  • $\begingroup$ Could you provide a starting point for this? Do I need to expand everything? I am really stuck still. $\endgroup$
    – Kyle Liu
    Commented Jun 11 at 6:16
  • $\begingroup$ There are 6 variables (4 latin, 2 greek) but 4 equations. This cannot be solved as such. $\endgroup$
    – R. J. Mathar
    Commented Jun 11 at 8:26
  • $\begingroup$ I just want to solve for d, c, alpha, and beta (4 variables). I'm confused which other two variables there are $\endgroup$
    – Kyle Liu
    Commented Jun 11 at 8:35

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