Final answer:
To determine the solutions to the system of linear inequalities, substitute the values of x and y from each point into the inequalities and check if the inequalities hold true. Four points (3, 1), (4, 2), (5, 3), and (6, 4) are solutions to the system of linear inequalities.
Step-by-step explanation:
To determine which points are solutions to the system of linear inequalities, we need to substitute the values of x and y from each point into the inequalities and check if the inequalities hold true.
Let's consider the system of inequalities:
y <= 2x + 1
y >= x - 1
a) (3, 1):
Substituting x = 3 and y = 1 into the inequalities:
1 <= 2(3) + 1 (True)
1 >= 3 - 1 (True)
Both inequalities hold true, so point (3, 1) is a solution.
b) (4, 2):
Substituting x = 4 and y = 2 into the inequalities:
2 <= 2(4) + 1 (True)
2 >= 4 - 1 (True)
Both inequalities hold true, so point (4, 2) is a solution.
c) (5, 3):
Substituting x = 5 and y = 3 into the inequalities:
3 <= 2(5) + 1 (True)
3 >= 5 - 1 (True)
Both inequalities hold true, so point (5, 3) is a solution.
d) (6, 4):
Substituting x = 6 and y = 4 into the inequalities:
4 <= 2(6) + 1 (True)
4 >= 6 - 1 (True)
Both inequalities hold true, so point (6, 4) is a solution.
e) (7, 5):
Substituting x = 7 and y = 5 into the inequalities:
5 <= 2(7) + 1 (False)
5 >= 7 - 1 (True)
The first inequality does not hold true, so point (7, 5) is not a solution.
The solutions to the system of linear inequalities are: (3, 1), (4, 2), (5, 3), and (6, 4).