The system of inequalities in the graph is:
y ≥ (1/2)*x - 2
y < 2x + 4
How to identify the system of inequalities?
Let's identify each one.
First the dashed line, we can see that the line is dashed and the region shaded is below that line, then we have:
y < line.
That line has an y-intercept at y = 4, so:
y = ax + 4
And it passes through (2, 0), so:
0 = a*2 + 4
-4/2 = a
-2 = a
The first inequality is:
y < 2x + 4
Now the second one, here we have a solid line, and the region shaded is above the line, so now we have:
y ≥ line.
This line has an y-intercept of -2, so:
y = ax - 2
And it passes through (4, 0), then:
0 = a*4 - 2
2/4 = a
1/2 = a
This inequality is:
y ≥ (1/2)*x - 2