Answer:
[tex]\left\{\begin{array}{l}y\ge 2x+4\\ \\y<-x+2\end{array}\right.[/tex]
Step-by-step explanation:
1. The solid line passes trough the points (0,4) and (-2,0). The equation of this line is:
[tex]\dfrac{x-0}{-2-0}=\dfrac{y-4}{0-4}\\ \\y-4=2x\\ \\y=2x+4[/tex]
The origin doesn't belong to the shaded region, so its coordinates do not satisfy the inequality. Thus,
[tex]y\ge 2x+4[/tex]
2. The dotted line passes trough the points (0,2) and (2,0). The equation of this line is:
[tex]\dfrac{x-0}{2-0}=\dfrac{y-2}{0-2}\\ \\y-2=-x\\ \\y=-x+2[/tex]
The origin belongs to the shaded region, so its coordinates satisfy the inequality. Thus,
[tex]y< -x+2[/tex]
Hence, the system of two inequalities is
