Question

Which point is a solution for the simultaneous inequalities:

y≤4x−5


y<2x−7


(1 point)
Responses

(7, 12)
(7, 12)

(5, 3)
(5, 3)

(0,15)
(0,15)

(15,0)

Answer 1

To find which point is a solution for the simultaneous inequalities \( y \leq 4x - 5 \) and \( y < 2x - 7 \), we can substitute each point into both inequalities.

Let's check each point:

1. **Point (7, 12)**

- For \( y \leq 4x - 5 \):
- \( 12 \leq 4(7) - 5 \)
- \( 12 \leq 28 - 5 \)
- \( 12 \leq 23 \) (True)

- For \( y < 2x - 7 \):
- \( 12 < 2(7) - 7 \)
- \( 12 < 14 - 7 \)
- \( 12 < 7 \) (False)

- So (7, 12) does not satisfy both inequalities.

2. **Point (5, 3)**

- For \( y \leq 4x - 5 \):
- \( 3 \leq 4(5) - 5 \)
- \( 3 \leq 20 - 5 \)
- \( 3 \leq 15 \) (True)

- For \( y < 2x - 7 \):
- \( 3 < 2(5) - 7 \)
- \( 3 < 10 - 7 \)
- \( 3 < 3 \) (False)

- So (5, 3) does not satisfy both inequalities.

3. **Point (0, 15)**

- For \( y \leq 4x - 5 \):
- \( 15 \leq 4(0) - 5 \)
- \( 15 \leq 0 - 5 \)
- \( 15 \leq -5 \) (False)

- So (0, 15) does not satisfy both inequalities.

4. **Point (15, 0)**

- For \( y \leq 4x - 5 \):
- \( 0 \leq 4(15) - 5 \)
- \( 0 \leq 60 - 5 \)
- \( 0 \leq 55 \) (True)

- For \( y < 2x - 7 \):
- \( 0 < 2(15) - 7 \)
- \( 0 < 30 - 7 \)
- \( 0 < 23 \) (True)

- So (15, 0) satisfies both inequalities.

Putting it all together, the only point that satisfies both inequalities is **(15, 0)**.