The paper deals with a solution of a fuzzy interval system of linear equations, i.e. a system in which fuzzy intervals (numbers) appear instead of crisp numbers. We obtain general results and then use them for finding the united solution set in the case when all fuzzy interval occurring in the system have the trapezoidal shape. Key words: fuzzy number, fuzzy interval, interval analysis, fuzzy arithmetic, fuzzy class theory, united solution set 1991 MSC: 03B52, 65G40