Answer:
Option D [tex]y\leq -3x-3[/tex] and [tex]y<-\frac{1}{2}x+2[/tex]
Step-by-step explanation:
step 1
Find the equation of the inequality A
we know that
The solution of the inequality A (dashed line) is the shaded area below the dashed line
The equation of the dashed line is [tex]y=-\frac{1}{2}x+2[/tex]
therefore
The equation of the inequality A is [tex]y<-\frac{1}{2}x+2[/tex]
step 2
Find the equation of the inequality B
we know that
The solution of the inequality B (solid line) is the shaded area below the solid line
The equation of the solid line is [tex]y=-3x-3[/tex]
therefore
The equation of the inequality B is [tex]y\leq -3x-3[/tex]
The system of linear inequalities is
[tex]y\leq -3x-3[/tex] and [tex]y<-\frac{1}{2}x+2[/tex]
