Unit 2 Solving Equations & Inequalities

Transcription

1 Coordinate Algebra Unit Solving Equations & Inequalities Name: Date: Unit Review Solve each system of linear equations by the given method. 1. Solve by Substitution: 5y 9 x y. Solve by Substitution: 15y 1 x 5y. Solve by Elimination: y y 15. Solve by Elimination: x y 5 x y 5. Solve by Graphing: 1 y y. Solve by Graphing: y y

2 Coordinate Algebra Unit Review Sheet 7. Solve by any method: y y Solve by any method: y y Sketch the graph of each linear inequality. For #, graph the system of inequalities showing the solutions. 1 y < x y x +. y x

3 Coordinate Algebra Unit Review Sheet Free Response Questions: SHOW ALL YOUR WORK 11. Alyssa needs $5.00 to buy some ice cream. The only money she has is a jar of dimes and quarters. a. Write an equation in standard form for the different amounts of dimes, d, and quarters, q, she could use. b. If Alyssa has quarters, how many dimes will she need to buy the ice cream? 1. Ike is having a party but doesn t have much time to make food. He decides to stop at Pizza Hut for some pizza and wings. A large pizza is $, while the wings will cost him $. a. Write an inequality for the cost, C, of buying pizza, p, and wings, w, if Ike has $50 to spend. b. If he buys pizzas, does he have enough money for boxes of wings? Explain your answer. 1. A package of hot dogs cost $ and a package of hamburger cost $. You bought a total of 11 packages of meat and you spent $5. How many packages of hamburger meat did you buy? Use a system to solve. 1. Tickets to an all-star game cost $.00 for children under twelve and $5.00 for everyone else. If 90 tickets were sold and $ was collected, how many children s tickets were sold? Use a system to solve. Multiple Choice: Choose the best answer for each question. 15. The ordered pair (5, 9) is a solution of which linear system? A. y 1 y 11 B. y y 9 C. x y y 19 D. y 1 y 1 1. What is the solution of the following linear system? y 1 7 y A. (-, 9) A. (, 5) B. (, 9) C. No Solution

4 Coordinate Algebra Unit Review Sheet 17. You are taking a test worth 0 points. There are a total of total questions consisting of five-point questions and two-point questions. How many five-point questions are on the test? A. A. 1 B. 15 C Which system of inequalities is graphed here? A. y 5 y B. y 5 y C. y 5 y D. y 5 y 19. If a system of linear equations has no solution, what do you know about the graphs of the equations? A. The graphs coincide B. The graphs intersect C. The graphs are parallel D. The graphs are perpendicular 0. Which region should be shaded to show the solution set of the system of inequalities below? A. Region A B. Region B C. Region C D. Region D x y 1. Asia is solving a system of equations using the substitution method. What is her first step? A. Isolate a variable in one equation B. Graph the first equation C. Eliminate a variable in one equation D. Solve each equation for y

5 Coordinate Algebra Unit Review Sheet. The graph below represents the price of taxis. According to the graph, when does it make more sense to take the blue cab and why? A. You will take the blue cab when you are going less than miles because it will be faster. B. You will take the blue cab when you are going more than miles because it will cost less. C. You will take the blue cab when you are going less than miles because it will cost less. D. You will take the blue cab miles because will not work as well. Yellow Car Blue Car Match the properties with the example that goes with it.. Commutative Property of Addition I. If a = b and b = c, then a = c. Associative Property of Addition J. + + = Symmetric Property of Equality K. a + 0 = a. Transitive Property of Equality L. ( + 9) + 5 = + (9 + 5) 7. Identity Property of Addition M. If a = b, then b = a Write the reason for each step in solving the equation. Equation Steps (x ) + = 5 Original Equation x + = 5. x + = 5 Simplify x = 1 9. x = 7 0.

6 Coordinate Algebra Unit Review Sheet Solve the following equation, and list the properties that you are using in each step. Equation Steps x = x + Original Equation Challenge: Sketch the graph of the following system of linear inequalities and name solutions y 5y y