Answer:
1. No
2. No
3. Yes
4. No
5. Yes
Step-by-step explanation:
Given the systems of linear inequalities: y < -2x + 1 and y ≤ x - 1:
In order to determine whether the given ordered pairs are solutions to the system, you could simply substitute their values into both inequality statements to see whether the ordreed pairs will satisfy both linear inequalities in the given system.
1) (0, 1)
y < -2x + 1
1 < -2(0) + 1
1 < 0 + 1
1 < 1 (False statement).
y ≤ x - 1
1 ≤ 0 - 1
1 ≤ - 1 (False statement).
Therefore, (0, 1) is not a solution.
2) (1, 2)
y < -2x + 1
2 < -2(1) + 1
2< -2 + 1
2 < - 1 (False statement).
y ≤ x - 1
2 ≤ 1 - 1
2 ≤ 0 (False statement).
Therefore, (1, 2) is not a solution.
3) (0, -1)
y < -2x + 1
-1 < -2(0) + 1
-1 < 0 + 1
-1 < 1 (True statement).
y ≤ x - 1
- 1 ≤ 0 - 1
- 1 ≤ - 1 (True statement).
Therefore, (0, 1) is a solution, as it satisfies both linear inequality statements.
4) (-1, -1)
y < -2x + 1
-1 < -2(-1) + 1
- 1 < 2 + 1
- 1 < 3 (True statement).
y ≤ x - 1
-1 ≤ -1 - 1
- 1 ≤ -2 (False statement).
Therefore, (-1, -1) is not a solution because the ordered pair only satisfies one of the linear inequalities, and not both.
5) (2, -4)
y < -2x + 1
-4 < -2(2) + 1
-4 < -4 + 1
-4 < -3 (True statement).
y ≤ x - 1
-4 ≤ 2 - 1
-4 ≤ 1 (True statement).
Therefore, (2, -4) is a solution.
