The solution set of the graph is attached below.
Explanation:
The given inequalities are [tex]y<-x+4[/tex] and [tex]y\geq \frac{2}{5} x-1[/tex]
We need to determine the graph that represents the solution set of the two inequalities.
Let us consider the inequality [tex]y<-x+4[/tex]
Substituting the coordinate [tex](0,0)[/tex] in the equality [tex]y<-x+4[/tex], we have,
[tex]0<0+4[/tex]
[tex]0<4[/tex]
Thus, the coordinate satisfies the inequality [tex]y<-x+4[/tex] , let us shade the region of the graph that contains the coordinate [tex](0,0)[/tex]
Now, we shall consider the inequality [tex]y\geq \frac{2}{5} x-1[/tex]
Substituting the coordinate [tex](0,0)[/tex] in the equality [tex]y\geq \frac{2}{5} x-1[/tex], we have,
[tex]0\geq \frac{2}{5} (0)-1[/tex]
[tex]0\geq -1[/tex]
Hence, the coordinate satisfies the inequality [tex]y\geq \frac{2}{5} x-1[/tex] , let us shade the region of the graph that contains the coordinate [tex](0,0)[/tex]
Thus, the intersection of the two regions of the inequalities is the solution set of the inequalities [tex]y<-x+4[/tex] and [tex]y\geq \frac{2}{5} x-1[/tex]
