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Unit Three Algebra II Practice Test Systems of Linear Equations & Inequalities Name______________________________________________Period_____Date______________ NON-CALCULATOR SECTION Vocabulary: Define each word and give an example. 1. System of Linear Inequalities 2. Objective Function 3. Inconsistent System of Equations Short Answer: 4. Explain how to tell if a linear system has one, none, or infinitely many solutions when solving it algebraically. 5. What is the first step for solving a system of linear equations by linear combinations? 6. Solve the equation. Check your solution(s): 7. Write the standard form of the equation of the line that passes through the points 8. The variables x and y vary directly, and y 25 when Review: 3 x 1 6 24 x 15 . Write an equation that relates the variables. Problems: **Be sure to show all work used to obtain your answer. Circle or box in the final answer.** 9. Graph the following linear systems and solve: a. 2x y 9 3x y 1 1, 4 and 3, 9 . b. Page 1 of 5 x 2y 6 2 x 4 y 12 Unit Three Algebra II Practice Test 10. Solve the linear system using the substitution method: Systems of Linear Equations & Inequalities 2 y x 3 7 x 3 y 21 1 x y 5 11. Solve the linear system using the linear combinations (elimination) method: 2 x 2 y 3 1 x 3y 6 2 12. Solve the linear system (any method): 1 x 5 y 3 3 2x 3y 2z 1 13. Solve the system: x 4 y z 7 3 x y 3 z 2 14. Graph the system of inequalities: x y 3 a. 2x y 5 3x y 5 b. y 1 x 1 Page 2 of 5 Unit Three Algebra II Practice Test Systems of Linear Equations & Inequalities 15. Find the minimum and maximum values of the objective function subject to the given constraints. Objective Function: C 5 x 2 y Constraints: x 0 2 x y 10 y 2 x 3 y 3 16. A store sells two brands of CD players. To meet customer demand, it is necessary to stock at least twice as many CD players of brand A as of brand B. It is also necessary to have at least 10 of brand B available. In the store there is room for no more than 50 players. Write a system of inequalities to describe the ways to stock the two brands. Multiple Choice Questions: Circle the best answer. 17. Solve the following linear system. 5x 2 y 8 5 y x3 2 A. B. 0, 4 0, 4 C. Infinitely many solutions D. No solution 18. What is the x-coordinate of the solution to the following system of equations? 2x y z 5 x 3 y 14 2 x 3 y 2 z 2 A. 14 B. 5 C. 1 D. 2 Page 3 of 5 Unit Three Algebra II Practice Test Systems of Linear Equations & Inequalities 19. Using linear programming procedures, the equation C 4 x 7 y is to be maximized subject to the following constraints: x0 y0 x y2 3 x 4 y 8 2 y 5 x 10 The grid may be used to sketch the feasible region. What is the minimum value for the objective function? A. 51 B. 14 C. 8 D. 0 Page 4 of 5 Unit Three Algebra II Practice Test Systems of Linear Equations & Inequalities Name______________________________________________Period_____Date______________ CALCULATOR SECTION 20. A ballet company says that 540 tickets have been sold for its upcoming performance. Tickets for the Orchestra seats are $56. Tickets for the Balcony seats are $38. The company has sold $24,120 in tickets. How many Orchestra and Balcony seats were sold? 21. Solve the linear system using your graphing calculator: 3x 4.02 y 9 y 3.1x 30.8 22. You are sewing doll clothes to sell at a craft show. Party dresses take 2.5 hours to make while casual sets take 1 hour. You make a profit of $9.00 on each party dress and $4.00 on each casual set. If you have no more than 30 hours available to sew and can make at most 15 outfits to sell, how many of each kind should you sew to maximize your profit? Objective Function: Constraints: Vertices of Feasible Region: Maximum Profit: Page 5 of 5