Is 'by' correctly used in the two given sentences? What about 'according' in the first sentence?

Is 'by' correctly used in the two given sentences? What about 'according' in the first sentence?

1. The man holding a questionnaire in his hands has indicated his answer by putting a check according to the given response codes.

2. The boy holding a questionnaire in his hands has supplied the needed data by writing his answer on the blank.