Answer:
Observe the attached image.
Step-by-step explanation:
We have the following linear inequalities
[tex]y > \frac{2}{3}x + 3\\\\y \leq \frac{1}{3}x + 2[/tex]
Graph the lines corresponding to each inequality
[tex]y > \frac{2}{3}x + 3[/tex] → [tex]y = \frac{2}{3}x + 3[/tex]
Cut with the y axis:
y = 3
Cut with the x axis:
[tex]0 = \frac{2}{3}x + 3[/tex]
[tex]-3 = \frac{2}{3}x[/tex]
[tex]x = -4.5[/tex]
[tex]y \leq \frac{1}{3}x + 2[/tex] → [tex]y = \frac{1}{3}x +2[/tex]
Cut with the y axis:
y = 2
Cut with the x axis:
[tex]0 = \frac{1}{3}x + 2[/tex]
[tex]-2 = \frac{1}{3}x[/tex]
[tex]x = -6[/tex]
Now graph the two lines
For [tex]y > \frac{2}{3}x + 3[/tex]
The region is made up of all the points that are above the line [tex]y =\frac{2}{3}x + 3[/tex]
For [tex]y \leq \frac{1}{3}x + 2[/tex]
The region is made up of all the points that are on the line and below [tex]y = \frac{1}{3}x +2[/tex]
The final region will be the interception of both regions
Observe the attached image.
The system shown in the image you attached is:
[tex]y > \frac{2}{3}x + 3\\\\y \leq -\frac{1}{3}x + 2[/tex]
