Question

Which point is a solution for the simultaneous inequalities and ?
(1 point)
y > −2x + 3 y < 3x − 3
(3, 6)
(1, −5)
(10, 5)
(2, 5)

Answer 1

To determine which point is a solution for the simultaneous inequalities \( y > -2x + 3 \) and \( y < 3x - 3 \), we can substitute each point into the inequalities and check if they satisfy both conditions.

1. **Point (3, 6)**:
- Check \( y > -2x + 3 \):
\[ 6 > -2(3) + 3 \]
\[ 6 > -6 + 3 \]
\[ 6 > -3 \] (True)
- Check \( y < 3x - 3 \):
\[ 6 < 3(3) - 3 \]
\[ 6 < 9 - 3 \]
\[ 6 < 6 \] (False)

2. **Point (1, -5)**:
- Check \( y > -2x + 3 \):
\[ -5 > -2(1) + 3 \]
\[ -5 > -2 + 3 \]
\[ -5 > 1 \] (False)

3. **Point (10, 5)**:
- Check \( y > -2x + 3 \):
\[ 5 > -2(10) + 3 \]
\[ 5 > -20 + 3 \]
\[ 5 > -17 \] (True)
- Check \( y < 3x - 3 \):
\[ 5 < 3(10) - 3 \]
\[ 5 < 30 - 3 \]
\[ 5 < 27 \] (True)

4. **Point (2, 5)**:
- Check \( y > -2x + 3 \):
\[ 5 > -2(2) + 3 \]
\[ 5 > -4 + 3 \]
\[ 5 > -1 \] (True)
- Check \( y < 3x - 3 \):
\[ 5 < 3(2) - 3 \]
\[ 5 < 6 - 3 \]
\[ 5 < 3 \] (False)

### Conclusion:
The point that satisfies both inequalities is **(10, 5)**.