Question

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

Answer 1

To determine which point is a solution to the simultaneous inequalities \( y > 3x + 1 \) and \( y \leq 2x + 5 \), we can analyze the inequalities.

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

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

A solution to the simultaneous inequalities must be in the region where both conditions are satisfied:

- The point must be above the line \( y = 3x + 1 \).
- The point must be on or below the line \( y = 2x + 5 \).

Without a specific graph or points provided, you would need to test any given points (x, y) against both inequalities to find a point that fulfills both conditions.

For example:
- Suppose you have the point (1, 5).
- Check \( y > 3x + 1 \): \( 5 > 3(1) + 1 \) → \( 5 > 4 \) (True)
- Check \( y \leq 2x + 5 \): \( 5 \leq 2(1) + 5 \) → \( 5 \leq 7 \) (True)

Since both conditions are satisfied, (1, 5) is a solution to the simultaneous inequalities.

If you have specific points from a graph you would like to check, please provide them, and I can help verify which one is a solution!