To determine if the point (3,8) is a solution to the simultaneous inequalities \( y > x + 5 \) and \( y \leq 6x - 3 \), we can evaluate each inequality separately with the point \( (3, 8) \).
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Check the first inequality \( y > x + 5 \):
- Substitute \( x = 3 \) and \( y = 8 \): \[ 8 > 3 + 5 \implies 8 > 8 \]
- This is false, as \( 8 \) is not greater than \( 8 \); instead, it is equal.
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Check the second inequality \( y \leq 6x - 3 \):
- Substitute \( x = 3 \) and \( y = 8 \): \[ 8 \leq 6(3) - 3 \implies 8 \leq 18 - 3 \implies 8 \leq 15 \]
- This is true.
Now we've determined:
- The point \( (3, 8) \) is not a solution for the inequality \( y > x + 5 \).
- The point \( (3, 8) \) is a solution for the inequality \( y \leq 6x - 3 \).
In conclusion, since \( (3, 8) \) is not a solution to both inequalities, the correct response is:
No, it is in the solution set for \( y \leq 6x - 3 \), but on the line for \( y > x + 5 \).