On a television game show, contestants earn 5 points for each correct answer, but lose 2 points for each wrong answer. On last week's show, the winning contestant earned 80 points and answered 30 questions. Given that x represents the number of questions answered correctly, and y represents the number of questions answered incorrectly, determine which system of equations correctly represents this situation.
A. 5x-2y=30
x+y=80
B. 5x-2y+80
x+y=30
C. 5x+2y=80
x-y=30
D. 5x+2y=30
x+y=80