Question

Which of the following points is a solution to the system of linear inequalities? -5x+y<-2 2x+y_>(equal or >)-9 A. (–7, –1) B. (–1, –7) C. (3, 5) D. (0, 3)

Answer 1

`-5x+y\ \textless \ -2 \\ 2x+y \geq -9 \\ \\ y\ \textless \ 5x-2 \\ y \geq -2x-9 \\ \\ -2x-9 \leq y \ \textless \ 5x-2`

Plug the values (x,y) into the inequality and check:

`A. (-7,-1) \\ -2 * (-7) -9 \leq -1 \ \textless \ 5 * (-7) -2 \\ 14-9 \leq -1 \ \textless \ -35-2 \\ 5 \leq -1 \ \textless \ -37 \\ not \ true`


`B. (-1,-7) \\ -2 * (-1) -9 \leq -7 \ \textless \ 5 * (-1) -2 \\ 2-9 \leq -7 \ \textless \ -5-2 \\ -7 \leq -7 \ \textless \ -7 \\ not \ true`


`C. (3,5) \\ -2 * 3 -9 \leq 5 \ \textless \ 5 * 3 -2 \\ -6-9 \leq 5 \ \textless \ 15-2 \\ -15 \leq 5 \ \textless \ 13 \\ true`


`D.(0,3) \\ -2 * 0 - 9 \leq 3 \ \textless \ 5 * 0 -2 \\ -9 \leq 3 \ \textless \ -2 \\ not \ true`

The answer is C.