To determine which point is a solution to the simultaneous inequalities \( y < 12x \) and \( y > 13x + 3 \), we need to evaluate each point against the inequalities.
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Point (25, 12):
- For \( y < 12x \): \[ 12 < 12 \times 25 \quad \text{(True, since 12 < 300)} \]
- For \( y > 13x + 3 \): \[ 12 > 13 \times 25 + 3 \quad \text{(False, since 12 > 328)} \]
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Point (10, 5):
- For \( y < 12x \): \[ 5 < 12 \times 10 \quad \text{(True, since 5 < 120)} \]
- For \( y > 13x + 3 \): \[ 5 > 13 \times 10 + 3 \quad \text{(False, since 5 > 133)} \]
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Point (2, 2):
- For \( y < 12x \): \[ 2 < 12 \times 2 \quad \text{(True, since 2 < 24)} \]
- For \( y > 13x + 3 \): \[ 2 > 13 \times 2 + 3 \quad \text{(False, since 2 > 29)} \]
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Point (3, 6):
- For \( y < 12x \): \[ 6 < 12 \times 3 \quad \text{(True, since 6 < 36)} \]
- For \( y > 13x + 3 \): \[ 6 > 13 \times 3 + 3 \quad \text{(False, since 6 > 42)} \]
After checking all points, none of the provided points satisfy both inequalities:
- \( (25, 12) \): satisfies \( y < 12x \) but not \( y > 13x + 3 \)
- \( (10, 5) \): satisfies \( y < 12x \) but not \( y > 13x + 3 \)
- \( (2, 2) \): satisfies \( y < 12x \) but not \( y > 13x + 3 \)
- \( (3, 6) \): satisfies \( y < 12x \) but not \( y > 13x + 3 \)
It appears that there is no valid point among the options given that satisfies both inequalities.