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.

5x-2y =80

x+y=30

Step-by-step explanation:

Basically, 5x is the points earned by correct questions (5 points per right answer) and -2x is the points lost by wrong answers (2 points taken away for every wrong answer). The total points the contestant earned is 80, which is why we set this equation equal to 80. Hence, 5x-2y=80.

They also tell us that the contestant answered a total of 30 questions, so x and y combined would be the total number of questions. Hence, x+y=30.