中文摘要：

以一种统一的模式给出了一般区间线性系统的弱可解和强可解的Farkas形式的充要条件．文章的结论不仅包含了已有文献中分别建立的区间线性系统的弱可解和强可解的各种Farkas型定理作为特例，而且也给出了以前结果所不能刻画的各种区间线性系统的Farkas型条件，为一般区间线性优化问题的最优性条件的探讨提供了理论基础．

英文摘要：

feasibility problems, In interval linear systems, combining weak and strong solvability or of interval linear equations or inequalities, we have eight different decision including weak solvability of equations, strong feasibility of inequalities and so on, All Farkas-type theorems for eight decisions problems of interval linear systems are established separately, since equivalent transformation between the interval linear systems are generally impossible due to dependency. In this paper, we consider about the general interval linear systems consisting of mixed equations and inequalities with mixed free and sign-restricted variables, and generalize the Farkas-type necessary and sufficient conditions for weak and strong solvability to a unified framework. Each particular result of Farkas-type results established separately for weak and strong solvability and feasibility of interval linear systems is a special case of our general approach. Besides, a concrete example is presented to illustrate our main results. It is known that the classical Farkas lemma and its various generalized versions are often used to characterize the optimality conditions of optimization problems. Thus, the interval version Farkas lemma may apply to characterize the optimality conditions of interval optimization problems.