Question

Which of the points shown on the graph is a solution to the simultaneous inequalities y>3x+1
𝑦
>
3
𝑥
+
1
and y≤2x+5
𝑦
≤
2
𝑥
+
5
? Write the x-value first and the y-value second.

Answer 1

To find a solution for the simultaneous inequalities \( y > 3x + 1 \) and \( y \leq 2x + 5 \), we need to determine the region that satisfies both conditions.

1. **Inequality \( y > 3x + 1 \)**:
- This represents the region above the line \( y = 3x + 1 \).

2. **Inequality \( y \leq 2x + 5 \)**:
- This represents the region below or on the line \( y = 2x + 5 \).

The solution to the simultaneous inequalities will be the intersection of the two regions defined by these inequalities. To find a specific point that satisfies both inequalities, you can test various points in the graph.

### Steps to find a solution:
- Identify several points (or use specific points you have on your graph).
- Check if the point satisfies both inequalities.

If you provide some points or their coordinates, I would be more than happy to verify whether or not they are indeed solutions to the given inequalities! If points from a graph are visible to you, choose any point that lies in the shaded region created by both inequalities.