IV. Look Back

The shaded region in the graph represents the solution set where both inequalities are satisfied. By examining the graph, we confirm that the region where $x \geq 2$ and $y \geq -\frac{3}{5}x + 3$ overlap is indeed shaded, meaning this is the solution set for the system.

Would you like a further breakdown of any steps or additional questions?

1. How would the solution change if $3x + 5y \leq 15$?
2. What happens if we add another inequality, like $y \leq x + 1$?
3. How does the solution set vary if $x \geq 4$ instead of $x \geq 2$?
4. How could you use this technique to solve a real-world optimization problem?
5. What if we introduced a third dimension to the inequalities?

Tip: When solving systems of inequalities, always verify each shaded region carefully to ensure the final solution set is correct.