Answer:
The correct option is 2.
Step-by-step explanation:
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 given graph it is clear that the solid line passes through the points (0,2) and (1,0). So, the related equation of solid line is
[tex]y-2=\frac{0-2}{1-0}(x-0)[/tex]
[tex]y-2=-2x[/tex]
Add 2 on both sides.
[tex]y=-2x+2[/tex]
The sign of inequality must be ≤ because the points on the line are included in the solution set and the shaded region is below the line.
[tex]y\leq -2x+2[/tex] .... (1)
From the given graph it is clear that the solid line passes through the points (0,-1) and (1,0). So, the related equation of solid line is
[tex]y-(-1)=\frac{0-(-1)}{1-0}(x-0)[/tex]
[tex]y+1=x[/tex]
Subtract 1 from both sides.
[tex]y=x-1[/tex]
The sign of inequality must be < because the points on the line are not included in the solution set and the shaded region is below the line.
[tex]y<x-1[/tex] .... (2)
The system of inequalities is
[tex]y\leq -2x+2[/tex]
[tex]y<x-1[/tex]
Therefore, the correct option is 2.
