Question

Which of the following points shows a solution to the simultaneous inequalities y>12x+5
and y<−2x+1
?(1 point)
Responses

(1,5.5)
left parenthesis 1 comma 5.5 right parenthesis

(−1.6,4.2)
left parenthesis negative 1.6 comma 4.2 right parenthesis

(−5,5)
left parenthesis negative 5 comma 5 right parenthesis

(4,8)

Answer 1

To find which point shows a solution to the simultaneous inequalities \( y > 12x + 5 \) and \( y < -2x + 1 \), we need to check each point against both inequalities.

1. **Point (1, 5.5)**
- Check \( y > 12x + 5 \):
- \( 5.5 > 12(1) + 5 \)
- \( 5.5 > 12 + 5 \)
- \( 5.5 > 17 \) (False)
- This point does not satisfy the first inequality.

2. **Point (-1.6, 4.2)**
- Check \( y > 12x + 5 \):
- \( 4.2 > 12(-1.6) + 5 \)
- \( 4.2 > -19.2 + 5 \)
- \( 4.2 > -14.2 \) (True)
- Check \( y < -2x + 1 \):
- \( 4.2 < -2(-1.6) + 1 \)
- \( 4.2 < 3.2 + 1 \)
- \( 4.2 < 4.2 \) (False)
- This point does not satisfy the second inequality.

3. **Point (-5, 5)**
- Check \( y > 12x + 5 \):
- \( 5 > 12(-5) + 5 \)
- \( 5 > -60 + 5 \)
- \( 5 > -55 \) (True)
- Check \( y < -2x + 1 \):
- \( 5 < -2(-5) + 1 \)
- \( 5 < 10 + 1 \)
- \( 5 < 11 \) (True)
- This point satisfies both inequalities.

4. **Point (4, 8)**
- Check \( y > 12x + 5 \):
- \( 8 > 12(4) + 5 \)
- \( 8 > 48 + 5 \)
- \( 8 > 53 \) (False)
- This point does not satisfy the first inequality.

After evaluating all points, the point that satisfies both inequalities is **(-5, 5)**.