Which point lies in the solution region of 4x+y≤16?

Correct answer: (3,3)

The governing rule is that a point belongs to the solution region of 4x+y≤16 exactly when substitution makes the inequality true. Test every option: for (5,0), 4x+y=20, so 20≤16 is false. For (0,20), the value is 20, again false. For (3,3), the value is 4(3)+3=12+3=15, and 15≤16 is true; therefore this point lies in the required half-plane. For (4,2), the value is 16+2=18, so it is also outside. Since only one option satisfies the inequality, option C is the unambiguous answer. The boundary itself would be represented by 4x+y=16, but the selected point is strictly inside the solution side because its value is less than 16.