To find which point on the graph is a solution to the inequalities \( y \leq 16x - 6 \) and \( y > 23x - 6 \), we need to evaluate each given point:
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Point (3, 6):
- For \( y \leq 16x - 6 \): \[ 6 \leq 16(3) - 6 \implies 6 \leq 48 - 6 \implies 6 \leq 42 \quad \text{(True)} \]
- For \( y > 23x - 6 \): \[ 6 > 23(3) - 6 \implies 6 > 69 - 6 \implies 6 > 63 \quad \text{(False)} \]
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Point (0, -6):
- For \( y \leq 16x - 6 \): \[ -6 \leq 16(0) - 6 \implies -6 \leq -6 \quad \text{(True)} \]
- For \( y > 23x - 6 \): \[ -6 > 23(0) - 6 \implies -6 > -6 \quad \text{(False)} \]
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Point (2, -12):
- For \( y \leq 16x - 6 \): \[ -12 \leq 16(2) - 6 \implies -12 \leq 32 - 6 \implies -12 \leq 26 \quad \text{(True)} \]
- For \( y > 23x - 6 \): \[ -12 > 23(2) - 6 \implies -12 > 46 - 6 \implies -12 > 40 \quad \text{(False)} \]
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Point (-10, -10):
- For \( y \leq 16x - 6 \): \[ -10 \leq 16(-10) - 6 \implies -10 \leq -160 - 6 \implies -10 \leq -166 \quad \text{(False)} \]
- For \( y > 23x - 6 \): \[ -10 > 23(-10) - 6 \implies -10 > -230 - 6 \implies -10 > -236 \quad \text{(True)} \]
None of the points satisfy both inequalities simultaneously. However, point (3, 6) is the only one that makes the first inequality true; alternatively, point (-10, -10) satisfies the second inequality.
Since none satisfy both, please verify whether there are conditions or specific instructions that may have been missed. But according to the evaluation, no solutions meet both criteria from the given options.
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