Algebra-1

Question Analysis
This question tests the student's ability to convert a real-world scenario into a system of inequalities.

Key Concept Explanation
A system of inequalities is used to represent multiple constraints (limits or requirements) on variables.
In this context:
"No more than" translates to the inequality symbol "≤" (less than or equal to).
"At least" translates to the inequality symbol "≥" (greater than or equal to).
Additionally, since hours cannot be negative, the variables x and y must be non-negative (x ≥ 0, y ≥ 0), though this is often implied in real-world problems involving time.

Step-by-step Solution
Total hours constraint: The student can spend no more than 10 hours on homework and sports combined.
This means the sum of study hours (x) and sports hours (y) is less than or equal to 10: 
Homework requirement: The student must study at least 4 hours, so study hours (x) are greater than or equal to 4: