This paper discusses conditions under which the state equations of large scale systems are uniquely determined and have well defined solutions. Usually the state equations of large scale systems must satisfy differential equations and algebraic equations simultaneously. Hence the problem is reduced to the solvability of differential-algebraic equations. The paper also discusses the effects of differential-algebraic equations on the optimization of large scale systems. A certain matrix plays an important role, and a generalized implicit function theorem which allows discontinuity turns out to be useful.