To determine which point is a solution to the simultaneous inequalities \(y < 12x\) and \(y > 13x + 3\), we need to substitute each of the proposed points into the inequalities.
-
Point (3, 6):
- For \(y < 12x\):
\(6 < 12(3) \implies 6 < 36\) (True) - For \(y > 13x + 3\):
\(6 > 13(3) + 3 \implies 6 > 39 + 3 \implies 6 > 42\) (False)
- For \(y < 12x\):
-
Point (10, 5):
- For \(y < 12x\):
\(5 < 12(10) \implies 5 < 120\) (True) - For \(y > 13x + 3\):
\(5 > 13(10) + 3 \implies 5 > 130 + 3 \implies 5 > 133\) (False)
- For \(y < 12x\):
-
Point (25, 12):
- For \(y < 12x\):
\(12 < 12(25) \implies 12 < 300\) (True) - For \(y > 13x + 3\):
\(12 > 13(25) + 3 \implies 12 > 325 + 3 \implies 12 > 328\) (False)
- For \(y < 12x\):
-
Point (2, 2):
- For \(y < 12x\):
\(2 < 12(2) \implies 2 < 24\) (True) - For \(y > 13x + 3\):
\(2 > 13(2) + 3 \implies 2 > 26 + 3 \implies 2 > 29\) (False)
- For \(y < 12x\):
After evaluating all points, none of them satisfy both inequalities simultaneously. Thus, if you are looking for a point that meets both conditions, there is no solution among the provided options.