Grade 12 Math: Inequalities and System of Equations

Grade 12 Math: Inequalities and System of Equations

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Solve the following system of linear equations:

x + y + z = 6 2x - y + 3z = 11 -x + 2y - z = 2

2. Which of the following graphs represents the inequality 2x - 3y < 6?

3. Graph the solution set for the following system of inequalities:

y > 2x - 4 y ≤ -x + 3

4. In linear programming, the region that satisfies all constraints is called the   region.

5. The points at which the boundary lines of the feasible region intersect are called   points.

6. True or False: When multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality sign.

7. A company manufactures two types of products, A and B. Product A requires 2 hours of labor and 1 hour of machine time. Product B requires 1 hour of labor and 3 hours of machine time. The company has a maximum of 100 hours of labor and 150 hours of machine time available per week. Write a system of inequalities to represent the constraints on the number of products A (x) and B (y) that can be manufactured.