Truncated Dyson-Schwinger equations represent finite subsets of the equations of motion for Green's functions. Solutions to these nonlinear integral equations can account for nonperturbative correlations. A closed set of coupled Dyson-Schwinger equations for the propagators of gluons and ghosts in Landau gauge QCD is obtained by neglecting all contributions from irreducible 4-point correlations and by implementing the Slavnov-Taylor identities for the 3-point vertex functions. We solve this coupled set in an one-dimensional approximation which allows for an analytic infrared expansion necessary to obtain numerically stable results. This technique, which was also used in our previous solution of the gluon Dyson-Schwinger equation in the Mandelstam approximation, is here extended to solve the coupled set of integral equations for the propagators of gluons and ghosts simultaneously. In particular, the gluon propagator is shown to vanish for small spacelike momenta whereas the previously neglected ghost propagator is found to be enhanced in the infrared. The running coupling of the nonperturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling, cec --~ 9.5.