Let's analyze the system of linear inequalities given in the image:

1. First inequality: $2x + y \leq 4$
2. Second inequality: $x \geq -5$
3. Third inequality: $y \leq 3$

Steps to graph the solution:

1. Graph the boundary line for $2x + y = 4$:

   • First, find the intercepts.
     • x-intercept: Set $y = 0$ in $2x + 0 = 4$, giving $x = 2$.
     • y-intercept: Set $x = 0$ in $2(0) + y = 4$, giving $y = 4$.
   • Draw the line passing through the points $(2, 0)$ and $(0, 4)$.
   • Since the inequality is $2x + y \leq 4$, shade the region below this line.

2. Graph the boundary for $x = -5$:

   • This is a vertical line at $x = -5$.
   • Since the inequality is $x \geq -5$, shade the region to the right of this line.

3. Graph the boundary for $y = 3$:

   • This is a horizontal line at $y = 3$.
   • Since the inequality is $y \leq 3$, shade the region below this line.

4. Find the region of overlap:

   • The solution to the system of inequalities is the region where all three shaded areas overlap.

Would you like me to graph this for you? Or do you have questions about any of the steps?

Here are 5 related questions for further exploration:

1. How do we determine which side of the line to shade in an inequality graph?
2. What is the significance of the boundary lines in inequality graphs?
3. How does the intersection of shaded regions help find the solution to a system of inequalities?
4. How would the graph change if one of the inequalities was strict, such as $2x + y < 4$?
5. What are the steps to solve a system of linear inequalities algebraically?

Tip: When graphing linear inequalities, always start by graphing the boundary lines and then decide which region to shade based on the inequality signs.