Graph the solution set of the system of inequalities.
x plus y
less than
negative 5
x plus y
less than
1

The graph above shows the solution set for the system of inequalities:

1. \( x + y < -5 \) (shaded in blue)
2. \( x + y < 1 \) (shaded in green)

The purple region represents the overlap, which is the solution set for the system. This is where both inequalities are satisfied simultaneously.

Would you like any further details or have any questions about this?

Here are 5 related questions to explore:

1. How do we find the intersection points between two boundary lines?
2. What changes when one of the inequalities is non-strict (e.g., \( x + y \leq -5 \))?
3. How would the graph look if we used \( x - y \) instead of \( x + y \)?
4. What if the inequality signs were reversed (e.g., \( x + y > -5 \))?
5. How do systems of inequalities apply to optimization problems?

**Tip:** Always check whether the boundary lines should be solid (for \( \leq \) or \( \geq \)) or dashed (for \( < \) or \( > \)) when graphing inequalities.

Discover how to graph the solution set for the system of inequalities x + y < -5 and x + y < 1. This lesson covers key algebraic concepts, including graphing inequalities and identifying their intersection. Suitable for students in Grades 9-12.

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