To determine which of the given ordered pairs are solutions for the inequality \( y > -2x + 8 \), we will plug in each ordered pair into the inequality and check if it holds true.
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For the pair \( (2, -12) \): \[ y = -12, \quad x = 2 \] Substitute into the inequality: \[ -12 > -2(2) + 8 \] Simplifying the right side: \[ -12 > -4 + 8 \] \[ -12 > 4 \quad \text{(False)} \]
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For the pair \( (-1, 14) \): \[ y = 14, \quad x = -1 \] Substitute into the inequality: \[ 14 > -2(-1) + 8 \] Simplifying the right side: \[ 14 > 2 + 8 \] \[ 14 > 10 \quad \text{(True)} \]
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For the pair \( (4, 2) \): \[ y = 2, \quad x = 4 \] Substitute into the inequality: \[ 2 > -2(4) + 8 \] Simplifying the right side: \[ 2 > -8 + 8 \] \[ 2 > 0 \quad \text{(True)} \]
Based on the checks above, the solutions for the inequality \( y > -2x + 8 \) are:
- \( (-1, 14) \)
- \( (4, 2) \)
So the two ordered pairs that are solutions for the inequality are \((-1, 14)\) and \((4, 2)\).