Question

Which point is a solution for the simultaneous inequalities y>−2x+3
and y<3x−3
?

(1 point)
Responses

(2,5)
left parenthesis 2 comma 5 right parenthesis

(10,5)
left parenthesis 10 comma 5 right parenthesis

(3,6)
left parenthesis 3 comma 6 right parenthesis

(1,−5)

Answer 1

To determine which point is a solution for the simultaneous inequalities \( y > -2x + 3 \) and \( y < 3x - 3 \), we can evaluate each point:

1. **For the point (2, 5)**:
- Check \( y > -2x + 3 \):
\[
5 > -2(2) + 3 \\
5 > -4 + 3 \\
5 > -1 \quad \text{(True)}
\]
- Check \( y < 3x - 3 \):
\[
5 < 3(2) - 3 \\
5 < 6 - 3 \\
5 < 3 \quad \text{(False)}
\]
- This point does not satisfy both inequalities.

2. **For the point (10, 5)**:
- Check \( y > -2x + 3 \):
\[
5 > -2(10) + 3 \\
5 > -20 + 3 \\
5 > -17 \quad \text{(True)}
\]
- Check \( y < 3x - 3 \):
\[
5 < 3(10) - 3 \\
5 < 30 - 3 \\
5 < 27 \quad \text{(True)}
\]
- This point satisfies both inequalities.

3. **For the point (3, 6)**:
- Check \( y > -2x + 3 \):
\[
6 > -2(3) + 3 \\
6 > -6 + 3 \\
6 > -3 \quad \text{(True)}
\]
- Check \( y < 3x - 3 \):
\[
6 < 3(3) - 3 \\
6 < 9 - 3 \\
6 < 6 \quad \text{(False)}
\]
- This point does not satisfy both inequalities.

4. **For the point (1, -5)**:
- Check \( y > -2x + 3 \):
\[
-5 > -2(1) + 3 \\
-5 > -2 + 3 \\
-5 > 1 \quad \text{(False)}
\]
- This point does not satisfy both inequalities.

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