Question

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 (10,5) left parenthesis 10 comma 5 right parenthesis (2,2) left parenthesis 2 comma 2 right parenthesis (3,6)

Answer 1

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

### Inequalities:
1. \(y < 12x\)
2. \(y > 13x + 3\)

### Points to test:
1. \((25, 12)\)
2. \((10, 5)\)
3. \((2, 2)\)
4. \((3, 6)\)

### Testing each point:

1. **Point \((25, 12)\)**:
- Check \(y < 12x\):
\[
12 < 12(25) \implies 12 < 300 \quad \text{(True)}
\]
- Check \(y > 13x + 3\):
\[
12 > 13(25) + 3 \implies 12 > 325 + 3 \implies 12 > 328 \quad \text{(False)}
\]

2. **Point \((10, 5)\)**:
- Check \(y < 12x\):
\[
5 < 12(10) \implies 5 < 120 \quad \text{(True)}
\]
- Check \(y > 13x + 3\):
\[
5 > 13(10) + 3 \implies 5 > 130 + 3 \implies 5 > 133 \quad \text{(False)}
\]

3. **Point \((2, 2)\)**:
- Check \(y < 12x\):
\[
2 < 12(2) \implies 2 < 24 \quad \text{(True)}
\]
- Check \(y > 13x + 3\):
\[
2 > 13(2) + 3 \implies 2 > 26 + 3 \implies 2 > 29 \quad \text{(False)}
\]

4. **Point \((3, 6)\)**:
- Check \(y < 12x\):
\[
6 < 12(3) \implies 6 < 36 \quad \text{(True)}
\]
- Check \(y > 13x + 3\):
\[
6 > 13(3) + 3 \implies 6 > 39 + 3 \implies 6 > 42 \quad \text{(False)}
\]

### Conclusion:
None of the points satisfy both inequalities simultaneously. Hence, there is no solution among the provided options that meets both criteria.