To determine which point is a solution to the simultaneous inequalities \( y < 12x \) and \( y > 13x + 3 \), we need to evaluate each point against both inequalities.
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Point (2, 2):
- For \( y < 12x \): \[ 2 < 12(2) \Rightarrow 2 < 24 \quad \text{(True)} \]
- For \( y > 13x + 3 \): \[ 2 > 13(2) + 3 \Rightarrow 2 > 26 + 3 \Rightarrow 2 > 29 \quad \text{(False)} \]
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Point (3, 6):
- For \( y < 12x \): \[ 6 < 12(3) \Rightarrow 6 < 36 \quad \text{(True)} \]
- For \( y > 13x + 3 \): \[ 6 > 13(3) + 3 \Rightarrow 6 > 39 + 3 \Rightarrow 6 > 42 \quad \text{(False)} \]
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Point (25, 12):
- For \( y < 12x \): \[ 12 < 12(25) \Rightarrow 12 < 300 \quad \text{(True)} \]
- For \( y > 13x + 3 \): \[ 12 > 13(25) + 3 \Rightarrow 12 > 325 + 3 \Rightarrow 12 > 328 \quad \text{(False)} \]
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Point (10, 5):
- For \( y < 12x \): \[ 5 < 12(10) \Rightarrow 5 < 120 \quad \text{(True)} \]
- For \( y > 13x + 3 \): \[ 5 > 13(10) + 3 \Rightarrow 5 > 130 + 3 \Rightarrow 5 > 133 \quad \text{(False)} \]
None of the points satisfy both inequalities \( y < 12x \) and \( y > 13x + 3 \). Therefore, it appears that none of the provided options are solutions to the simultaneous inequalities.
If the graph image is available, please make sure to confirm the arrangement of the lines, as the above analysis is based solely on the algebraic interpretation of the inequalities given.