To determine if the point \( (1, 2) \) is a solution to the system of inequalities, we will substitute \( x = 1 \) and \( y = 2 \) into each inequality and check if the inequalities hold true.
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First Inequality: \( 4x + y \geq 6 \) \[ 4(1) + 2 \geq 6 \] \[ 4 + 2 \geq 6 \] \[ 6 \geq 6 \quad \text{(True)} \]
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Second Inequality: \( 4x + 3y > 10 \) \[ 4(1) + 3(2) > 10 \] \[ 4 + 6 > 10 \] \[ 10 > 10 \quad \text{(False)} \]
Since the point \( (1, 2) \) satisfies the first inequality but does not satisfy the second inequality, it is not a solution to the system of inequalities.
In conclusion, \( (1, 2) \) is not a solution to the system of inequalities.