Abstract:The solvability of the following three-dimensional product-type system of difference equationswhere a, b, c, d, f , g ∈ Z, α, β, γ ∈ C \ {0} and x −i , y −i , z −i ∈ C \ {0}, i ∈ {0, 1}, is shown. This is the first three-dimensional system of the type with multipliers for which formulas are presented for their solutions in closed form in all the cases.