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We introduce a class of hyperfields which includes several constructions ofnon-quotient hyperfields. We then use it to partially answer a question posedby M. Baker and T. Zhang: Does a system of homogeneous linear equations withmore unknowns than equations always have a nonzero solution? We also consider aclass of hyperfields that was claimed in the literature to be non-quotient, andshow that this is false.

Nontrivial solutions for homogeneous linear equations over some non-quotient hyperfields