Answer:
Option D.
Step-by-step explanation:
Consider the below figure attached with this question.
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the below figure it is clear that the a solid line passes through the points (-2,0) and (0,4). So, the equation of related line is
[tex]y-0=\frac{4-0}{0-(-2)}(x-(-2))[/tex]
[tex]y=2(x+2)[/tex]
[tex]y=2x+4[/tex]
[tex]-2x+y=4[/tex]
All area above the solid line is shaded. It means the sign of inequality is ≥.
[tex]-2x+y\geq 4[/tex]
From the below figure it is clear that the a dashed line passes through the points (2,0) and (0,2). So, the equation of related line is
[tex]y-0=\frac{2-0}{0-(2)}(x-(2))[/tex]
[tex]y=-1(x-2)[/tex]
[tex]y=-x+2[/tex]
[tex]x+y=2[/tex]
All area below the dashed line is shaded. It means the sign of inequality is <.
[tex]x+y<2[/tex]
System of inequality is
[tex]-2x+y\geq 4[/tex]
[tex]x+y<2[/tex]
Therefore, the correct option is D.
