The problem in the image involves solving a system of two linear inequalities graphically. The first step asks to graph the solution set of the first inequality, which is given as:

$x > 2 \text{ or } y \geq 7$

Here’s how to approach it:

Step-by-Step Explanation:

1. Graphing the Inequality $x > 2$:

• The line $x = 2$ is a vertical line, and since the inequality is $x > 2$, the region to the right of this line needs to be shaded.
• For the boundary:
  • The line is dashed because the inequality is strict (i.e., it does not include $x = 2$).
  • Enter two points on this vertical line, such as:
    • Point 1: $(2, -10)$
    • Point 2: $(2, 10)$
• Select the region to the right of this line for shading (this will be the shaded region for $x > 2$).

2. Graphing the Inequality $y \geq 7$:

• The line $y = 7$ is a horizontal line.
• The inequality $y \geq 7$ includes the line, so the line should be solid.
• The region above the line $y = 7$ needs to be shaded.
• Enter two points on this horizontal line, such as:
  • Point 1: $(-10, 7)$
  • Point 2: $(10, 7)$

Shading the Region:

• The solution to the system of inequalities involves the union of the regions for $x > 2$ and $y \geq 7$.
• For $x > 2$, shade to the right of the dashed vertical line.
• For $y \geq 7$, shade above the solid horizontal line.

Would you like further details on this or how to proceed with the graph?

Here are 5 related questions to expand on this:

1. How do you determine if a boundary line should be solid or dashed?
2. What is the difference between $x > 2$ and $x \geq 2$ in graphical terms?
3. How do you graph a compound inequality involving "or" versus "and"?
4. How do you find the intersection of two shaded regions for a system of inequalities?
5. What happens if the inequalities involve $<$ or $>$ for both $x$ and $y$?

Tip: Always remember to label your boundary lines clearly and distinguish between dashed and solid lines for strict vs. inclusive inequalities.