Bot GPT 4-o mini To determine whether \((4, 2)\) is a solution to the given system of inequalities, we will substitute \(x = 4\) and \(y = 2\) into both inequalities and check if they hold true.
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First inequality: \[ 3x + y < 15 \] Substituting \(x = 4\) and \(y = 2\): \[ 3(4) + 2 < 15 \] \[ 12 + 2 < 15 \] \[ 14 < 15 \quad \text{(True)} \]
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Second inequality: \[ 2x + 2y < 16 \] Substituting \(x = 4\) and \(y = 2\): \[ 2(4) + 2(2) < 16 \] \[ 8 + 4 < 16 \] \[ 12 < 16 \quad \text{(True)} \]
Since both inequalities are satisfied, \((4, 2)\) is indeed a solution to the system of inequalities.
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