To determine which point is a solution to the simultaneous inequalities \( y < 12x \) and \( y > 13x + 3 \), we will evaluate each point in the inequalities.
-
Point (25, 12)
- For \( y < 12x \):
\( 12 < 12(25) \)
\( 12 < 300 \) (True) - For \( y > 13x + 3 \):
\( 12 > 13(25) + 3 \)
\( 12 > 325 + 3 \)
\( 12 > 328 \) (False)
- For \( y < 12x \):
-
Point (2, 2)
- For \( y < 12x \):
\( 2 < 12(2) \)
\( 2 < 24 \) (True) - For \( y > 13x + 3 \):
\( 2 > 13(2) + 3 \)
\( 2 > 26 + 3 \)
\( 2 > 29 \) (False)
- For \( y < 12x \):
-
Point (3, 6)
- For \( y < 12x \):
\( 6 < 12(3) \)
\( 6 < 36 \) (True) - For \( y > 13x + 3 \):
\( 6 > 13(3) + 3 \)
\( 6 > 39 + 3 \)
\( 6 > 42 \) (False)
- For \( y < 12x \):
-
Point (10, 5)
- For \( y < 12x \):
\( 5 < 12(10) \)
\( 5 < 120 \) (True) - For \( y > 13x + 3 \):
\( 5 > 13(10) + 3 \)
\( 5 > 130 + 3 \)
\( 5 > 133 \) (False)
- For \( y < 12x \):
None of the points satisfy both inequalities; however, if you're looking for a point that satisfies one or the other, the closest examination shows that:
- Point (3, 6) satisfies \( y < 12x \) only.
Since none of the options satisfy both inequalities, it can be concluded that all points fail at some point. If you were meant to select a point for one of the inequalities, then (3, 6) would at least satisfy \( y < 12x \) but not both conditions.
Please check the provided conditions and the visual information from your image to ensure the details are accurate to assess if a solution exists with the parameters given.
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