To determine if the point \((5, 2)\) is a solution to the given system of inequalities, we need to substitute \(x = 5\) and \(y = 2\) into each inequality and check whether the resulting statements are true.
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For the first inequality:
\[ 16x + 14y > 11 \] Substitute \(x = 5\) and \(y = 2\): \[ 16(5) + 14(2) > 11 \] This simplifies to: \[ 80 + 28 > 11 \] \[ 108 > 11 \] This statement is true. -
For the second inequality:
\[ 19x + y \leq 3 \] Substitute \(x = 5\) and \(y = 2\): \[ 19(5) + 2 \leq 3 \] This simplifies to: \[ 95 + 2 \leq 3 \] \[ 97 \leq 3 \] This statement is false.
Since the point \((5, 2)\) satisfies the first inequality but does not satisfy the second inequality, it is not a solution to the system of inequalities.