This paper deals with the construction of exact and analytical-numerical solutions with a priori error bounds for systems of the type u_t = Au_xx, A₁u(0, t) + B₁u_x (0, t) = 0, A₂u (1, t) + B₂u_x (1, t) = 0, 0 < x < 1, t > 0, u(x, 0) = f(x), where A₁, A₂, B₁ and B₂ are matrices for which no simultaneous diagonalizable hypothesis is assumed, and A is a positive stable matrix. Given an admissible error ε and a bounded subdomain D, an approximate solution whose error with respect to an exact series solution is less than ε uniformly in D is constructed.