Solution
Given the following:
[tex]\begin{cases}x>2 \\ y<5 \\ 2x+y>6\end{cases}[/tex]
when x is greater than 2
[tex]x=3,4,5,\ldots\ldots[/tex]
when y is less than 5
[tex]y=0,1,2,3,4,\ldots\ldots[/tex]
Therefore the best option is when x = 3 and y = 2
[tex]\begin{gathered} x=3,y=2 \\ 2x+y>6 \\ 2(3)+2=8 \\ 8>6 \end{gathered}[/tex]
it is correct because 8 is greater than 6
Therefore the best option is (3, 2)
Hence the correct answer is Option C
