To determine if the point (3, 8) is a solution to the simultaneous inequalities \( y > x + 5 \) and \( y \leq 6x - 3 \), we need to check both inequalities one at a time.
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Check the first inequality \( y > x + 5 \): We substitute \( x = 3 \) and \( y = 8 \) into the inequality: \[ 8 > 3 + 5 \] Simplifying the right side: \[ 8 > 8 \] This inequality is not true because 8 is not greater than 8.
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Check the second inequality \( y \leq 6x - 3 \): We again substitute \( x = 3 \) and \( y = 8 \) into this inequality: \[ 8 \leq 6(3) - 3 \] Simplifying the right side: \[ 8 \leq 18 - 3 \] \[ 8 \leq 15 \] This inequality is true.
Since the point (3, 8) does not satisfy the first inequality but satisfies the second inequality, the point (3, 8) is not a solution to the simultaneous inequalities.
In conclusion:
- The point (3, 8) fails the first inequality \( y > x + 5 \), even though it satisfies the second inequality \( y \leq 6x - 3 \).
Thus, the final answer is that (3, 8) is NOT a solution to the simultaneous inequalities.