Answer:
[tex]x<-2\\\\y\leq-x-2[/tex]
Step-by-step explanation:
From the given graph , the shaded region is bounded by two lines ( one is dotted and another is solid line).
Dotted line : It is parallel to y-axis and intersecting the x -axis at .
so the equation of the line is x=-2.
But it is represented in dotted form it means the inequality sign used here is strictly less than.
i.e. the equation for dotted line = [tex]x<-2[/tex]
Solid line : It is passing through (-2,0) and (-1,-1).
Equation of line passing through (a,b) and (c,d) :-
[tex](y-a)=\dfrac{d-b}{c-a}(x-b)[/tex]
Then equation of sold line:
[tex](y-0)=\dfrac{-1-0}{-1-(-2)}(x-(-2))\\\\\Rightarrow\ y=\dfrac{-1}{-1+2}(x+2)\\\\\Rightarrow\ y=\dfrac{-1}{1}(x+2)\\\\\Rightarrow\ y=-x-2[/tex]
Hence, the inequality represents solid line(≤)= [tex]y\leq-x-2[/tex]
Hence, the system of linear inequalities is graphed will be :-
[tex]x<-2\\\\y\leq-x-2[/tex]
