To determine which point is a solution to the simultaneous inequalities \( y < 12x \) and \( y > 13x + 3 \), we need to evaluate each point provided.
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Point (3, 6):
- Check \( y < 12x \): \[ 6 < 12(3) \implies 6 < 36 \quad \text{(true)} \]
- Check \( y > 13x + 3 \): \[ 6 > 13(3) + 3 \implies 6 > 39 + 3 \implies 6 > 42 \quad \text{(false)} \]
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Point (25, 12):
- Check \( y < 12x \): \[ 12 < 12(25) \implies 12 < 300 \quad \text{(true)} \]
- Check \( y > 13x + 3 \): \[ 12 > 13(25) + 3 \implies 12 > 325 + 3 \implies 12 > 328 \quad \text{(false)} \]
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Point (10, 5):
- Check \( y < 12x \): \[ 5 < 12(10) \implies 5 < 120 \quad \text{(true)} \]
- Check \( y > 13x + 3 \): \[ 5 > 13(10) + 3 \implies 5 > 130 + 3 \implies 5 > 133 \quad \text{(false)} \]
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Point (2, 2):
- Check \( y < 12x \): \[ 2 < 12(2) \implies 2 < 24 \quad \text{(true)} \]
- Check \( y > 13x + 3 \): \[ 2 > 13(2) + 3 \implies 2 > 26 + 3 \implies 2 > 29 \quad \text{(false)} \]
None of the points satisfy both inequalities simultaneously. Thus, it appears there may have been an expectation of further values being possible or a misunderstanding of the original inequalities and constraints.
Given the choices available, none of the provided (3, 6), (25, 12), (10, 5), or (2, 2) work as solutions to the inequalities \( y < 12x \) and \( y > 13x + 3 \). Please check for possible mistakes, values outside the listed options, or further context surrounding the inequalities.