Use the graphing calculator tool to graph the following system of inequalities

`y>6x-3`

`y\le x+2`



Select all solutions to the system.

The graph above displays the system of inequalities:

1. \( y > 6x - 3 \) (represented by the red shaded region above the red line)
2. \( y \leq x + 2 \) (represented by the blue shaded region below the blue line)

The solution to this system of inequalities is the overlapping region where both conditions are satisfied: the area above the red line and below or on the blue line.

Would you like further details, or do you have any questions about interpreting the solution?

Here are 5 related questions to consider:

1. What happens if the inequality \( y \leq x + 2 \) changes to \( y < x + 2 \)?
2. How would the solution change if both inequalities were "greater than" inequalities?
3. How can we algebraically solve for specific points of intersection in this system?
4. What would the solution look like if one inequality used absolute value?
5. How would you graph inequalities with vertical or horizontal lines?

**Tip:** To solve systems of inequalities graphically, always look for regions where the shading of both inequalities overlaps!

Use the graphing calculator tool to graph the following system of inequalities: y > 6x - 3, y ≤ x + 2. Select all solutions to the system.

Learn how to graph and find the solution to the system of inequalities y > 6x - 3 and y ≤ x + 2. This tutorial covers key concepts in graphing inequalities, including identifying the solution regions and understanding the intersection of shaded areas. Suitable for students in Grades 8-10.

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