The ordered pairs that are solutions to the system of inequalities are (2,0), (3,2), and (4,5).
To find the solutions to the system of inequalities, consider both inequalities and identify the region of the coordinate plane that satisfies both conditions.
The system of inequalities is:
2x + 2y ≥ 7
y < 3x - 5
Now, let's examine the options for ordered pairs:
1. (1,2):
(2(1) + 2(2) = 6 < 7
(2 < 3(1) - 5 = -2
This point is not a solution.
2. (2,0):
2(2) + 2(0) = 4 < 7
0 < 3(2) - 5 = 1
This point is a solution.
3. (3,2):
2(3) + 2(2) = 10 ≥ 7
2 < 3(3) - 5 = 4
This point is a solution.
4. (4,5):
2(4) + 2(5) = 18 ≥ 7
5 < 3(4) - 5 = 7
This point is a solution.
Therefore, the ordered pairs that are solutions to the system of inequalities are (2,0), (3,2), and (4,5).