Mathematica: How to find conditions on parameters, for a system to admit solutions?

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How to find conditions on parameters, for a system to admit solutions?
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(mathematica.stackexchange.com/users/54979/florin)florin
(mathematica.stackexchange.com/users/53427/e-chan-l%c3%b3pez)E. Chan-López
(mathematica.stackexchange.com/users/7152/user64494)user64494
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If anything is off, please write me at peter D.O.T schneider A.T ois42.de

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