To determine if each ordered pair is a solution to a system of linear inequalities, we first need to know the specific inequalities in the system. Since the inequalities are not provided, I'll show you how to determine if an ordered pair is a solution based on hypothetical inequalities.
Let's assume the system of inequalities is as follows (example):
- \(y > 2x - 1\)
- \(y \leq -x + 2\)
Now, we will check each ordered pair against these inequalities:
-
(2, 1):
- For \(y > 2x - 1\): Is \(1 > 2(2) - 1\)? (1 > 3? False)
- For \(y \leq -x + 2\): Is \(1 \leq -2 + 2\)? (1 ≤ 0? False)
- Conclusion: Not a solution.
-
(0, 2):
- For \(y > 2x - 1\): Is \(2 > 2(0) - 1\)? (2 > -1? True)
- For \(y \leq -x + 2\): Is \(2 \leq -0 + 2\)? (2 ≤ 2? True)
- Conclusion: This is a solution.
-
(-4, 2):
- For \(y > 2x - 1\): Is \(2 > 2(-4) - 1\)? (2 > -9? True)
- For \(y \leq -x + 2\): Is \(2 \leq -(-4) + 2\)? (2 ≤ 6? True)
- Conclusion: This is a solution.
-
(-1, 2):
- For \(y > 2x - 1\): Is \(2 > 2(-1) - 1\)? (2 > -3? True)
- For \(y \leq -x + 2\): Is \(2 \leq -(-1) + 2\)? (2 ≤ 3? True)
- Conclusion: This is a solution.
-
(0, -2):
- For \(y > 2x - 1\): Is \(-2 > 2(0) - 1\)? (-2 > -1? False)
- For \(y \leq -x + 2\): Is \(-2 \leq -0 + 2\)? (-2 ≤ 2? True)
- Conclusion: Not a solution.
-
(-3, -2):
- For \(y > 2x - 1\): Is \(-2 > 2(-3) - 1\)? (-2 > -7? True)
- For \(y \leq -x + 2\): Is \(-2 \leq -(-3) + 2\)? (-2 ≤ 5? True)
- Conclusion: This is a solution.
Summary:
- (2, 1): Not a solution
- (0, 2): Solution
- (-4, 2): Solution
- (-1, 2): Solution
- (0, -2): Not a solution
- (-3, -2): Solution
If you have a specific system of inequalities to check the points against, please provide them, and we can ascertain which pairs are solutions accordingly.
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