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Unit 3 Exam REVIEW 1. Which of the following systems has the solution (-19, -14)? A 3x – 2y = –1 C 4x + y = 7 6x – 4y = 6 B –3x + 4y = 1 2x – 3y = 4 x + 4y = 4 D 3x – 4y = 2 –2x + 4y = 9 2. What are the vertices of the feasible region bounded by the constraints? 𝒙≥𝟎 𝒚≥𝟎 𝒚 ≤ −𝟐𝒙 + 𝟖 3. An astronomer has developed the following system of equations based on the paths of two asteroids in the same plane. At which coordinates do their paths intersect? Solve using elimination. 4x – 2y = 8 x + 2y = –3 4. Your friend wants to solve the system using elimination. 3x – 4 y = 1 5 x + 2 y = 7 Which is the best way for your friend to proceed? 5. Which is the solution to the system? 6x + 5y + 2z = 41 4x – 10z = – 10 – x – 2y + 2z = – 1 6. A student has 10 coins in her pocket that have a value of $0.85. The coins are either nickels or dimes. Which system of linear equations represents this scenario? F Give a solution and a non- solution to the system of linear inequalities. 7. y x – 3 x + y 2 8. Which system of linear equations does the graph show? x y = 0.85 0.5x + 0.10y = 10 x y = 10 0.5x + 0.10y = 0.85 x y = 0.10 H 5x + 10y = 0.85 G J x y = 0.85 5x + 10y = 10 y = 2x + 1 y = 3x 4 y = 2x + 1 B y = 3x 4 A y = 2x 1 y = 3x 4 y = 2x 1 D y = 3x 4 C 9. Graph the system and give the solution. x – 3y = – 6 x + y = – 2 11. What is the x-value in the solution to the system of linear equations? y 1 x 2 2 y – 3 x – 2 2 12. What is the x-value of the solution? 4x – 2y + 4z = –16 x + 2y – 3z = 9 3x – y – 4z = 3 10. A classmate graphed the system of linear equalities incorrectly, as shown. Which best describes his mistake? x – y –2 x + y –1 F The line that represents x – y ≥ –2 should be dotted. G He graphed the line x – y = –2 incorrectly. H He shaded the incorrect half plane for x + y > –1. J The region that represents the solution should be bounded by 4 sides. 13. List three methods used to solve systems of equations. Describe the strengths of each method. 14. Graph. y x 5 3 x y 2 inequalities. 23. ________________________ occur on the solid boundary lines of the shaded region. 24. Parallel lines have _____________ Solutions 25. Coinciding lines (the same two lines) have __________________ solutions. 26. Unit 2 Review What is the solution of 8 |2n + 8| = 16 15. The limits or restrictions are also called ________________________. 16. _________________________ is a method for finding a minimum or maximum value of some quantity, given a set of constraints. 17. On a graph, the_____________________ contains all of the points that satisfy the constraints. 27. Unit 2 Review Which inequality best describes the graph? 18. The ________________________ models a quantity that is related to the constraint variables. 19. The ________________________ of the feasible region are the points where the least and greatest values for the objective function occur. 28. Unit 2 Review. What type of symmetry does the absolute value parent function have? 20. The ____________________ is the solution to a system of equations when graphed. 29. Unit 1 Review. Over what line do inverses reflect? 21. _________________________ occur inside the shaded region of a system of inequalities. 30. Unit 1 Review. What are the intercepts for the cubic parent function? 22. _________________________ occur outside the shaded region of a system of