This time, you will solve and graph system of linear inequalities independently using Polya’s four step in

problem solving. I know you can do it!

1. {

3x + 5y ≥ 15

x ≥ 2

I. Understanding the Problem

II. Make a Plan.

III. Carry out the Plan.

IV. Look back

### 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?

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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.

This time, you will solve and graph a system of linear inequalities independently using Polya’s four steps in problem solving. I know you can do it!

1. {

3x + 5y ≥ 15

x ≥ 2

I. Understanding the Problem

II. Make a Plan.

III. Carry out the Plan.

IV. Look back

Learn to solve and graph the system of linear inequalities 3x + 5y ≥ 15 and x ≥ 2 using Polya’s four-step problem-solving method. This guide explains each step—understanding the problem, planning, execution, and reviewing—to ensure a thorough solution. Perfect for students in Grades 9-11.

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