If the cement floor is constructed the way I seen many original floors of homes your age the joists of the floor are beveled at the top 2" and there are ledgers on the sides of the joists, pieces of wood that hold other pieces of wood to fill in between the joists that create a surface to lay cement between the joists.

Typically where the joists are is where the cracks occur. The only way to keep the cracks from coming back is to remove all the cement, and depending on a few factors like thickness and depth of the joists, the span the joist make, you may be able to flatten the tops of the joists by 3/4" to add plywood over the tops of the flattened joists, but if the joists can't be reduced in depth to flatten the tops, then the joists need to be "sistered" to accept the new subfloor.
Either way it is not a simple patch and go on from there.