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Algebra 1: Systems Unit Review I. A-REI.5 Learning Target: I can prove that a linear combination (i.e. elimination) is valid. Name ______Answer Key_________ Date ____________________ Period _____ 5. Solve by elimination. 3 x 4 y 18 2 x y 3 1. Rachel wants to eliminate the x-variable to solve the system shown. What does she need to do before combining the equations? You do not have to solve. x 4 y 8 2x 6 y 4 Explain:__Multiply x 4 y 8 equation by -2 so that the x terms are opposite and will cancel out.____________ 2. Rachel wants to eliminate the x-variable to solve the system shown. What does she need to do before combining the equations? You do not have to solve. Answer: ____ 6,9 ____ 8 x 9 y 1 7 x 4 y 7 Explain:___ Multiply 8 x 9 y 1 equation by 7and the 7 x 4 y 7 equation by 8 so that the x terms will be the same number 56 but opposite sign to cancel out._____ 6. The Rodriguez family and the Wong family went to a brunch buffet. The restaurant charges one price for adults and another price for children. The Rodriguez family has two adults and four children and their bill was $52. The Wong family has three adults and one child, and their bill was $38. Write a system of equations to represent the situation. 3. Is (3, 2) a solution of the system? Prove your System: ___ 2a 4c 52 ____ answer. ____ 3a c 38 ___ 2 g 3h 0 3 g 2h 5 7. How much does the restaurant from problem #7 charge for children? For adults? Answer: _Solution____ 4. Is (-3, -5) a solution of the system? Prove your answer. 2 x y 1 3 x y 12 Answer: _The restaurant charges $8 for children Answer: _Not a Solution__ Algebra 1: Systems Unit Review Answer Key and $10 for adults. __________________________ 6/2/14 PUHSD Algebra Curriculum Team II. A-REI.6 Learning Target: Explain why the xcoordinate of the points where the graphs of the equations y=f(x) and y =g(x) intersect are solutions of the equations f(x) = g(x); find the solutions approximately. 9. Bethany and Calista are sisters who are racing against each other. Bethany starts at the starting line, while Calista starts a 1 mile ahead of the starting line. Calista runs 4 miles per hour, while Bethany runs 5 miles per hour. Part A: Write an equation for each sister. 8. The graph of a system of linear equations is shown below. Name the solution and explain how you know it’s a solution. Bethany:__ y 5 x _________ Calista:___ y 4 x 1 _________ Part B: Draw a graph plotting the progress of both runners in a 3-hour race. Solution: ___No Solution_______ Explain:__The lines never intersect therefore there no solution that would make both equations true._____ 8. Part A: Identify the point of intersection. y x 1 3 y x4 2 Part C: Who would win a ½ -hour race? A 1-hour race? A 6-hour race? Point of intersection: __ 2, 1 _____ ½ -Hour: __Calista___ Part B: Justify the x-coordinate from the point of 3 intersection is a solution of x 1 x 4 . 2 3 x 1 x 4 2 3 2 1 2 4 2 2 1 3 4 1-Hour: __Same_____ 3-Hour: __Bethany___ Part D: Who would win if both girls running pace were equal? Explain. Time in hours Answer: __If both girls kept the same 1 1 running pace, Calista would win because she has a mile head start.______________________ Algebra 1: Systems Unit Review Answer Key 6/2/14 PUHSD Algebra Curriculum Team III. F-LE.2 Learning Target: I can write a linear function given a pattern, a set of ordered pairs, a graph, or a slope and a point. 12. Write a system of equations represented by the tables below. Table A: 10. Write a system of equations represented by the graph below. x y -3 -1 1 2 3 11 5 -1 -4 -7 -2 -1 0 3 4 -6.5 -6.25 -6 -5.25 -5 Table B: x y System: ___ y System: ___ y 3 x 2 ___ 1 x 6 ____ 2 ___ y 0.25 x 6 ___ 3 ___ y x 2 ___ 2 13. Write a system of equations represented by the tables below. 11. Part A: Graph a system that has the solution (2, 4). Table A: x -2 -1 1 2 3 Answers may vary, but an example… y 1 2 4 5 6 Table B: x -3 0 1 2 3 y 12 6 4 2 0 Part B: Write the equations of the system that has the solution (2, 4). 1 x 5 ___ 2 System: ___ y x 3 ____ ___ y x 2 ______ _ y 2 x 6 ___ System: ___ y Algebra 1: Systems Unit Review Answer Key 6/2/14 PUHSD Algebra Curriculum Team 14. You have $290 in savings and save an additional $16 each week. Your brother has $430 in savings and spends $12 of his savings each week. Write a system of equations to represent the situation. 17. How many calories from problem #16 are in each? System: ___ S 16 w 290 ____ ____ y 2 x 6 _____ 15. After how many weeks from problem #14 will you and your brother have the same amount of savings and what amount of money will be in Answer: _ The ice Cream has 130 calories and each saving account when there the same? the pie has 370 calories. _____________________ 18. The manager of a movie theater wants to know the number of adults and children who go to the movies. The theater charges $8 for each adult ticket and $4 for each child ticket. At a showing where 200 tickets were sold, the theater collected $1304. Write a system of equations to represent the situation. System: ___ 8a 4c 1304 __ ____ a c 200 ___ 19. Find how many of each ticket from problem # 18 type were sold? Answer: __It will take 5 weeks when you and your brother will both have $370. __________________ 16. The number of calories in a piece of pie is 20 less than three times the number of calories in a scoop of ice cream. The pie and ice cream together have 500 calories. Write a system of equations to represent the situation. System: ___ P 3 I 20 ___ ___ P I 500 ___ Algebra 1: Systems Unit Review Answer Key Answer: _The movie theather sold 74 children tickets and 126 adults tickets . _________________ 6/2/14 PUHSD Algebra Curriculum Team IV. A-REI.12 Learning Target: I can graph the solution to one or more liner inequalities. 21. Write a system of linear inequalities that defines the shaded region. System: ___ y 1 x 2 ____ 2 25. Mina’s Catering Services is organizing a formal dinner for 280 people. The hall has two kinds of table, one type of table seats 4 people and and the other type of table seats 10 people. The hall can contain up to a total of 52 tables. Write a system of inequalities to represent the situation. System: ___ x y 52 ____ __ 4 x 10 y 280 _____ 26. Graph the system of inequalities to determine the possiple combinations of tables that can be used for the event so there are enough for all people. ___ y x 1 ________ Mina’s Catering Service 22. Write a system of linear inequalities that defines the shaded region. y 72 10 people tables 64 56 48 40 32 24 System: ___ y x ____ 16 ___ x 2 ___ 8 24. Part A: Graph the linear system of inequalities. 3x y 2 8 x 2 y 2 8 16 24 32 40 48 56 64 72 80 x 4 people tables Answer:__ Mina’s Catering Services needs to use 40 Which of the following are solutions to the system? a. (2, 2) b. (0, 0) c. (10, 1) d. ( 4, 5) tables that seat 4 people and 12 tables that seat 10 people in order to be able to seat all 280 people for dinner._____________________________________ Algebra 1: Systems Unit Review Answer Key 6/2/14 PUHSD Algebra Curriculum Team