To determine which point is a solution to the simultaneous inequalities \(y < 12x\) and \(y > 13x + 3\), let's analyze each inequality:
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For the inequality \(y < 12x\):
- This means that the point must lie below the line represented by \(y = 12x\).
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For the inequality \(y > 13x + 3\):
- This means that the point must lie above the line represented by \(y = 13x + 3\).
We'll evaluate each given point to check whether it satisfies both inequalities.
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Point (10, 5):
- \(y < 12x\): \(5 < 12(10)\) → \(5 < 120\) (True)
- \(y > 13x + 3\): \(5 > 13(10) + 3\) → \(5 > 130 + 3\) → \(5 > 133\) (False)
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Point (25, 12):
- \(y < 12x\): \(12 < 12(25)\) → \(12 < 300\) (True)
- \(y > 13x + 3\): \(12 > 13(25) + 3\) → \(12 > 325 + 3\) → \(12 > 328\) (False)
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Point (2, 2):
- \(y < 12x\): \(2 < 12(2)\) → \(2 < 24\) (True)
- \(y > 13x + 3\): \(2 > 13(2) + 3\) → \(2 > 26 + 3\) → \(2 > 29\) (False)
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Point (3, 6):
- \(y < 12x\): \(6 < 12(3)\) → \(6 < 36\) (True)
- \(y > 13x + 3\): \(6 > 13(3) + 3\) → \(6 > 39 + 3\) → \(6 > 42\) (False)
Upon checking all points, none of them satisfy both inequalities simultaneously. Therefore, if you had to select an answer based on further clarification or additional information regarding the inequalities or the coordinate plane, please do so.
If you were presented with a graphical representation, you might also be able to visually confirm which regions are included according to the inequalities. If we strictly follow the math:
- None of the provided points are a solution to the simultaneous inequalities \(y < 12x\) and \(y > 13x + 3\).
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