To determine which point is a solution to the inequalities \( y < 12x \) and \( y > 13x + 3 \), we will evaluate each of the given points against both inequalities.
-
Point (10, 5):
- Check \( y < 12x \):
- \( 5 < 12(10) \)
- \( 5 < 120 \) (True)
- Check \( y > 13x + 3 \):
- \( 5 > 13(10) + 3 \)
- \( 5 > 130 + 3 \)
- \( 5 > 133 \) (False)
- Check \( y < 12x \):
-
Point (2, 2):
- Check \( y < 12x \):
- \( 2 < 12(2) \)
- \( 2 < 24 \) (True)
- Check \( y > 13x + 3 \):
- \( 2 > 13(2) + 3 \)
- \( 2 > 26 + 3 \)
- \( 2 > 29 \) (False)
- Check \( y < 12x \):
-
Point (3, 6):
- Check \( y < 12x \):
- \( 6 < 12(3) \)
- \( 6 < 36 \) (True)
- Check \( y > 13x + 3 \):
- \( 6 > 13(3) + 3 \)
- \( 6 > 39 + 3 \)
- \( 6 > 42 \) (False)
- Check \( y < 12x \):
-
Point (25, 12):
- Check \( y < 12x \):
- \( 12 < 12(25) \)
- \( 12 < 300 \) (True)
- Check \( y > 13x + 3 \):
- \( 12 > 13(25) + 3 \)
- \( 12 > 325 + 3 \)
- \( 12 > 328 \) (False)
- Check \( y < 12x \):
Since none of the points satisfy both inequalities \( y < 12x \) and \( y > 13x + 3 \), it appears there is no solution among the provided options. If you need further assistance or clarification, feel free to ask!