To determine which ordered pairs are part of the solution set for the linear inequality \( y \geq -3x + 4 \), we need to check each ordered pair by substituting the \( x \) and \( y \) values into the inequality.
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For the pair \( (4, -1) \): \[ -1 \geq -3(4) + 4 \] \[ -1 \geq -12 + 4 \] \[ -1 \geq -8 \quad \text{(True)} \]
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For the pair \( (3, 0) \): \[ 0 \geq -3(3) + 4 \] \[ 0 \geq -9 + 4 \] \[ 0 \geq -5 \quad \text{(True)} \]
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For the pair \( (0, 3) \): \[ 3 \geq -3(0) + 4 \] \[ 3 \geq 0 + 4 \] \[ 3 \geq 4 \quad \text{(False)} \]
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For the pair \( (0, 2) \): \[ 2 \geq -3(0) + 4 \] \[ 2 \geq 0 + 4 \] \[ 2 \geq 4 \quad \text{(False)} \]
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For the pair \( (2, -2) \): \[ -2 \geq -3(2) + 4 \] \[ -2 \geq -6 + 4 \] \[ -2 \geq -2 \quad \text{(True)} \]
The ordered pairs that are part of the solution set for the inequality \( y \geq -3x + 4 \) are:
- \( (4, -1) \) (True)
- \( (3, 0) \) (True)
- \( (2, -2) \) (True)
Thus, the solution set includes \( (4, -1) \), \( (3, 0) \), and \( (2, -2) \).