Answer:
y > x - 4
x > 3
Explanation:
The system of inequalities need to represent the overlapped, black area, so you need to write an inequality for each of the two lines shown.
To find out whether you should be using a >, <, ≤, or ≥, identify on the graph first:
The vertical line is shaded to the right of the line. The line is also dashed, so it should be a >.
The sloped line is shaded above the line. The line is also dashed, so it should be a >.
Then, find the slopes of the lines.
Refer to the sloped line as Line 1 and the vertical line as Line 2.
The slope of Line 1 is 1. It's y-intercept (where the line crosses the y-axis) is -4.
So: y = x - 4
Replace the = with >.
y > x - 4
Line 2 is unidentified, so you can see that it's x = 3. Replace the = with >.
x > 3
You can always check by plugging in a point from the overlapped area, like (4, 1).
(4, 1)
y > x - 4
1 > 4 - 4
1 > 0
x > 3
4 > 3
These statements are true.