Final answer:
Nucleotide Excision Repair (NER) is the DNA repair system that does not involve the use of ligase activity. In NER, damaged bases are replaced by copying the template using DNA polymerase, and DNA ligase is not directly involved in the repair process.
Step-by-step explanation:
The DNA repair system that does NOT involve the use of ligase activity is Nucleotide Excision Repair (NER). In NER, damaged bases are removed along with a few bases on the 5' and 3' ends, and these are replaced by copying the template with the help of DNA polymerase. The ends of the newly synthesized fragment are attached to the rest of the DNA using DNA ligase, which creates a phosphodiester bond. However, in NER, ligase is not directly involved in the repair process.