To determine if the point (2, 5) is a solution to the system of inequalities, we need to check whether the coordinates \(x = 2\) and \(y = 5\) satisfy both inequalities.
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First inequality: \(y \geq x + 3\) \[ 5 \geq 2 + 3 \] \[ 5 \geq 5 \quad \text{(true)} \] So, (2, 5) satisfies the first inequality.
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Second inequality: \(y < 4x + 2\) \[ 5 < 4(2) + 2 \] \[ 5 < 8 + 2 \] \[ 5 < 10 \quad \text{(true)} \] So, (2, 5) also satisfies the second inequality.
Since the point (2, 5) satisfies both inequalities, we conclude that it is indeed a solution to the system of inequalities.