In this paper, we propose two strongly convergent algorithms which combines Mann iterative scheme, diagonal subgradient method, projection method and proximal method for solving split system of fixed point set constrained equilibrium problems in real Hilbert spaces. The computation of first algorthim requires prior knowledge of operator norm. The problem of finding or at least an estimate of the norm of an operator, in general, is not an easy task in Hilbert spaces. Based on the first algorithm, we propose another algorithm with a way of selecting the step-sizes such that its implementation does not need any prior information about the operator norm. The strong convergence properties of the algorithms are established under mild assumptions on equilibrium bifunctions.