We consider the existence, uniqueness and effectiveness of solutions to infinite systems of equations in certain inverse limits of algebras. The notion of a guarded infinite system of equations is defined and used to establish existence and uniqueness results about the solutions. A domain structure associated with the inverse limit is used to prove the theorems. The use of infinite systems of equations is illustrated by the study of infinite synchronous concurrent algorithms (ISCAs). An ISCA is an infinite network of processors, operating in parallel, and synchronised by a global clock; the algorithm processes infinite streams of data. The algorithms are described by infinite systems of equations and, since the networks are deterministic, the equations are required to have unique solutions.