Answer:
The solution set of given inequalities are represented by Part A.
Step-by-step explanation:
The given inequalities are
[tex]y\geq x+1[/tex]
[tex]y+x\geq -1[/tex]
The related equations of both inequalities are
[tex]y=x+1[/tex]
Put x=0, to find the y-intercept and put y=0, to find x intercept.
[tex]y=0+1\Rightarrow y=1[/tex]
[tex]0=x+1\Rightarrow x=-1[/tex]
Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,1).
Similarly, for the second related equation
[tex]y+x=-1[/tex]
[tex]y+0=-1\Rightarrow y=-1[/tex]
[tex]0+x=-1\Rightarrow x=-1[/tex]
Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,-1).
Now, join the x and y-intercepts of both lines to draw the line.
Now check the given inequalities by (0,0).
[tex]0\geq 0+1\Rightarrow 0\geq 1[/tex]
It is a false statement, therefore the shaded region is in the opposite side of origin.
[tex]0+0\geq -1\Rightarrow 0\geq -1[/tex]
It is a true statement, therefore the shaded region is about the origin.
From the below figure we can say that the solution set of given inequalities are represented by Part A.
