Which ordered pairs are in the solution set of the system of linear inequalities? y is greater than or equal to negative 1 third x plus 2 y is less than 2 x plus 3

Check each ordered pair against both inequalities: its y-value must be at least −⅓x + 2 and less than 2x + 3. For (3, 1), −⅓(3) + 2 = 1, so y = 1 meets the first inequality, and 1 < 2(3) + 3 = 9. For (4, 2), the first right-hand side is ⅔, so 2 ≥ ⅔, and 2 < 11; (2, 2) also satisfies both. Thus the set in choice D works.

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