Linear Inequalities – Two Variables & System of Inequalities

Grade 11 Maths — Linear Inequalities – Two Variables & System of Inequalities: 25 practice questions with instant scoring and explanations.

1. The inequality 2x + 3y > 6 represents:
2. The boundary line of x + y ≥ 5 is drawn as:
3. The boundary line of x + y < 5 is drawn as:
4. For inequality 3x - 2y ≤ 6, check if (0, 0) satisfies it:
5. For inequality x + 2y > 4, check if (2, 2) satisfies it:
6. The system {x ≥ 0, y ≥ 0} represents:
7. Solve the system: {x ≥ 0, y ≥ 0, x + y ≤ 4}. The vertices are:
8. The region for {x ≥ 1, y ≥ 1, x + y ≤ 5} forms a:
9. For the system {y ≥ x, y ≤ -x + 4}, the intersection region is:
10. The inequality y < 2x - 3 represents all points:
11. The inequality y ≥ -x + 2 represents all points:
12. A linear programming problem requires:
13. Maximize z = 3x + 2y subject to x ≥ 0, y ≥ 0, x + y ≤ 4. Maximum value is:
14. Minimize z = x + y subject to x ≥ 1, y ≥ 1, 2x + y ≥ 4. Minimum value is:
15. The feasible region for {x ≥ 0, y ≥ 0, 2x + y ≤ 4, x + y ≤ 3} has vertices at:
16. The inequality x < y graphically shows the region:
17. For {y ≤ x + 1, y ≥ x - 1}, the solution is all points:
18. In linear programming, the optimal solution occurs at:
19. The system {x ≤ 2, y ≤ 3} represents:
20. For 3x + 2y ≥ 6, the point (0, 0) is:
21. The solution to {x + y > 5, x - y < 1} is the region:
22. For the system with vertices (0,0), (4,0), (0,3), if z = 2x + 3y, then max value is:
23. The inequality |x| ≤ 2 and |y| ≤ 2 forms a region that is a:
24. For 2x - y ≤ 4, the point (3, 0) satisfies the inequality:
25. For 3x + 2y ≥ 6, the point (2, 0) satisfies the inequality: