Question

Use the image to answer the question.

A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 dashed lines with arrows at both ends are plotted, and various regions of the graph are marked.

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

(1 point)
Responses

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

(2,2)
left parenthesis 2 comma 2 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 evaluate each point in the inequalities.

1. **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)

2. **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)

3. **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)

4. **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)

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.