Answer :
[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.
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.
