[tex]-5x+y\ \textless \ -2 \\
2x+y \geq -9 \\ \\
y\ \textless \ 5x-2 \\
y \geq -2x-9 \\ \\
-2x-9 \leq y \ \textless \ 5x-2[/tex]
Plug the values (x,y) into the inequality and check:
[tex]A. (-7,-1) \\
-2 \times (-7) -9 \leq -1 \ \textless \ 5 \times (-7) -2 \\
14-9 \leq -1 \ \textless \ -35-2 \\
5 \leq -1 \ \textless \ -37 \\
not \ true[/tex]
[tex]B. (-1,-7) \\
-2 \times (-1) -9 \leq -7 \ \textless \ 5 \times (-1) -2 \\
2-9 \leq -7 \ \textless \ -5-2 \\
-7 \leq -7 \ \textless \ -7 \\
not \ true[/tex]
[tex]C. (3,5) \\
-2 \times 3 -9 \leq 5 \ \textless \ 5 \times 3 -2 \\
-6-9 \leq 5 \ \textless \ 15-2 \\
-15 \leq 5 \ \textless \ 13 \\
true[/tex]
[tex]D.(0,3) \\
-2 \times 0 - 9 \leq 3 \ \textless \ 5 \times 0 -2 \\
-9 \leq 3 \ \textless \ -2 \\
not \ true[/tex]
The answer is C.
