Question

Which point is a solution to the simultaneous inequalities y<12x
and y>13x+3
?

(1 point)
Responses

(2,2)
left parenthesis 2 comma 2 right parenthesis

(25,12)
left parenthesis 25 comma 12 right parenthesis

(3,6)
left parenthesis 3 comma 6 right parenthesis

(10,5)

Answer 1

To determine which point is a solution to the simultaneous inequalities \( y < 12x \) and \( y > 13x + 3 \), we will test each point.

1. **Point (2, 2)**:
- For the first inequality: \( 2 < 12(2) \) → \( 2 < 24 \) (True)
- For the second inequality: \( 2 > 13(2) + 3 \) → \( 2 > 26 + 3 \) → \( 2 > 29 \) (False)

2. **Point (25, 12)**:
- For the first inequality: \( 12 < 12(25) \) → \( 12 < 300 \) (True)
- For the second inequality: \( 12 > 13(25) + 3 \) → \( 12 > 325 + 3 \) → \( 12 > 328 \) (False)

3. **Point (3, 6)**:
- For the first inequality: \( 6 < 12(3) \) → \( 6 < 36 \) (True)
- For the second inequality: \( 6 > 13(3) + 3 \) → \( 6 > 39 + 3 \) → \( 6 > 42 \) (False)

4. **Point (10, 5)**:
- For the first inequality: \( 5 < 12(10) \) → \( 5 < 120 \) (True)
- For the second inequality: \( 5 > 13(10) + 3 \) → \( 5 > 130 + 3 \) → \( 5 > 133 \) (False)

None of the given points satisfy both inequalities simultaneously. Therefore, there is no solution among the provided options.