We deal with m-component vector-valued solutions to the Cauchy problem for a linear both homogeneous and nonhomogeneous weakly coupled second-order parabolic system in the layer R-T(n+1) = R-n x (0, T). We assume that coefficients of the system are real and depending only on t, n >= 1 and T < infinity. The homogeneous system is considered with initial data in [L-p(R-n)](m), 1 <= p <= infinity. For the nonhomogeneous system we suppose that the initial function is equal to zero and the right-hand side belongs to [L-p(R-T(n+1) )](m) boolean AND [C-alpha<((R-T(n+1)))over bar>](m), alpha is an element of (0, 1). Explicit formulas for the sharp coefficients in pointwise estimates for solutions to these problems and their directional derivative are obtained.