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ANSWER

Last option.

EXPLANATION

The equations of the lines are:

[tex]y = 2x + 1[/tex]

and

[tex]x + y = - 2[/tex]

We can quickly use the slope of the lines to determine which line they represent in the graph.

The slope of the first equation is 2, which is positive (y=2x+1)

This is the line that is tilted upwards, from left to right.

We can see that the upper half plane of the this line is shaded. Hence the inequality it represents is

y>2x+1

We used > and not ≥ because the line is a dashed line.

Also: x+y=-2 is obviously the second line.

We rewrite to get: y=-x-2. We can see that it has a negative slope.

The lower half of this line is shaded,hence the corresponding inequality is;

x+y<-2

Therefore the system of inequalities is:

y>2x+1

x+y<-2

The last choice is correct.