To determine the system of two inequalities which is represented by the graph, you have to do such steps:
1 step. The dashed blue line represents sign > or <. The line has the equation y=2x, then the inequality should be y>2x or y<2x. Since point (-1,1) belongs to the blue shaded region, then the inequallity y>2x is true.
2 step. The solid red line represents sign ≤ or ≥. The line has the equation x+2y=-8, then the inequality should be x+2y≤-8 or x+2y≥-8. Since the origin (0,0) doesn't belong to the red shaded region, then the inequallity x+2y≤-8 is true.
Thus, the system is
[tex]\left\{\begin{array}{l}y>2x\\x+2y\le-8.\end{array}\right.[/tex]
Answer: correct choice is A.
