In this paper we identify certain peculiar systems of 2 discrete-time evolution equations,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ilde x_n} = {F^{(n)}}(x1,{\\rm{x2),}}\\;\\;\\;{\\rm{n = 1,2,}}$$\\end{document}which are algebraically solvable. Here ℓ is the “discrete-time” independent variable taking integer values (ℓ = 0,1, 2,...), xn ≡ xn(ℓ) are 2 dependent variables, and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ilde x_n} \\equiv {x_n}(\\ell + 1)$$\\end{document} are the corresponding 2 updated variables. In a previous paper the 2 functions F(n)(x1,x2), n = 1, 2, were defined as follows: F(n)(x1,x2) = P2 (xn, xn+1), n = 1,2 mod [2], with P2 (x1, x2) a specific second-degree homogeneous polynomial in the 2 (indistinguishable!) dependent variables x1(ℓ) and x2(ℓ). In the present paper we further clarify some aspects of that model and we present its extension to the case when F(n)(x1,x2) = Qk(n)(x1,x2), n = 1, 2, with Qk(n)(x1,x2) a specific homogeneous function of arbitrary (integer) degree k (hence a polynomial of degree k when k > 0) in the 2 dependent variables x1 (ℓ) and x2 (ℓ).