In the present work for a limited period, we consider the system of integro-differential equations of containing the
parameter. The kernel of the integral term is assumed to be degenerate, and as additional conditions for finding the
values of the parameter and the solution of the given integro-differential equation, the values of the solution at the initial
and final points of the given segment are given. The boundary value problem under consideration is investigated by
D.S. Dzhumabaev's parametrization method. Based on the parameterization method, additional parameters are
introduced. For a fixed value of the desired parameter, the solvability of the special Cauchy problem for a system of
integro-differential equations with a degenerate kernel is established. Using the fundamental matrix of the differential
part of the integro-differential equation and assuming the solvability of the special Cauchy problem, the original
boundary value problem is reduced to a system of linear algebraic equations with respect to the introduced additional
parameters. The existence of a solution to this system ensures the solvability of the problem under study. An algorithm
for finding the solution of the initial problem based on the construction and solutions of a system of linear algebraic
equations is proposed.