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A simple graph is called equationally noetherian if any system of equations is equivalent to its finite subsystem. It isn't hard to notice that a simple graph is equationally noetherian if and only if it is equationally noetherian in one variable equations. Based on this property we described all equationally noetherian graphs with help of forbidden subgraphs (joint with Ivan Buchinsky). Also several examples of hypergraphs will be presented that are not equationally noetherian but equationally noetherian in one variable equations.