The work purpose is the estimation of an error of the solution of interval system of the linear algebraic equations (ISLAE) with interval factors of matrixes and components of the right parts in a narrow interval of their change on a basis of a "sign technique". The specialized algorithm is designed, allowing to find estimations of angular vectors of the solution of the formalized point systems, similar to results of "external" estimation of set of solutions ISLAE in interval algebra. The technique of the algebraic approach to the solution of systems of a different order is theoretically proved and is confirmed by numerical examples, in what degree quantitative uncertainty of the initial information makes qualitative impact on the solution.