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 [tex]$x$[/tex] represents the number of questions answered correctly, and [tex]$y$[/tex] represents the number of questions answered incorrectly, determine which system of equations correctly represents this situation.
A.
[tex]\[
\begin{array}{r}
5x - 2y = 30 \\
x + y = 80
\end{array}
\][/tex]
B.
[tex]\[
\begin{array}{r}
5x + 2y = 30 \\
x - y = 80
\end{array}
\][/tex]
C.
[tex]\[
\begin{array}{r}
5x - 2y = 80 \\
x + y = 30
\end{array}
\][/tex]
D.
[tex]\[
\begin{array}{r}
5x + 2y = 80 \\
x - y = 30
\end{array}
\][/tex]