To graph the system of linear inequalities:

1. First inequality: $y < x + 5$

   • This is the equation of a line with slope $1$ and y-intercept $5$. The graph of the line would be $y = x + 5$, but since it's a strict inequality (less than), you'll graph the line as dashed, and shade below the line because we are interested in the region where $y$ is less than $x + 5$.

2. Second inequality: $x + y < 4$

   • Rewrite it as $y < -x + 4$, which is the equation of a line with slope $-1$ and y-intercept $4$. Again, graph the line as dashed, and shade below the line because it's a "less than" inequality.

Steps to Graph:

• Plot the line $y = x + 5$ as a dashed line and shade the region below it.
• Plot the line $y = -x + 4$ as a dashed line and shade the region below it.
• The solution to the system is the region where the shaded areas overlap.

Would you like a visual representation of the graph?

Related Questions:

1. How do you find the intersection of two lines algebraically?
2. What happens if an inequality is "greater than or equal to" instead of "less than"?
3. How do we handle inequalities with vertical or horizontal lines?
4. How would the graph change if the slope of one line is negative?
5. How can you test a point to see if it lies in the solution region?

Tip:

When graphing inequalities, always remember that a dashed line indicates that the boundary is not included, while a solid line means it is.