In practice most computer-based accounting packages only simulate the appearance of a double-entry bookkeeping system. In traditional double-entry bookkeeping one must manually enter the data for each transaction into multiple journals: a minimum of twice, or more than twice for split transactions. This is what allows the journals to be cross-checked for consistency. The reports produced by computer-based "double-entry" systems will always be consistent, however, because they're really just different views of the same set of multi-account transactions recorded in a general ledger rather than distinct single-sided transactions recorded in account-specific journals.
"General-ledger accounting" (for lack of a better term) is superior in terms of having a single source of truth, but not very practical for manual accounting since all the transactions are mixed together. The introduction of computers changed all that by making it easy to generate targeted reports from the general ledger.