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Name: ______________________ Class: _________________ Date: _________ ID: A Systems of Equations Unit Test 1. What is the solution to the graphed system of equations? 2. Romell receives five points for each correct answer on a test and loses two point for each incorrect answer. a. Write an equation showing that Reggie received 30 points. b. Write an equation showing that Reggie answered all 35 questions on the test. ____ 3. Solve the system: 4x − y = 19 y= x − 1 a. no solution b. (5, 1) c. 4. Solve the system: 3x + 1 y = 10 3 5 − y = −2x + 35 3 1 ÊÁ 4, − 2 ˆ˜ Ë d. ÊÁ 6, 5 ˆ˜ Ë Name: ______________________ ID: A 5. Solve the system: 2x + 5y = 16 5x − 2y = 11 6. A group of 82 people attend a museum opening. There were two times as many adults as children in the group. Write a system of equations that you could use to solve this problem, where a is the number of adults and c is the number of children in the group. Solve the system of equations for c, the number of children in the group. 7. Solve the system: 2x + 5y = 12 x − 6y = −11 ____ 8. Which of the following systems of equations is ( a. x+y = 4 c. y = 3x + 1 b. 3 1 , 3 ) a solution to? 4 4 1 y=− x 3 3y − x = 0 1 y= x 3 d. 2x + 3y = 7 y + 3x = 6 x−y = 2 9. Your family is planning a birthday party for you and is getting it catered. Hamilton’s Catering charges $15 per person and Turasky’s Catering charges an initial fee of $50 and charges $10 per person. At what number of people is Hamilton’s Catering the cheaper option? Show all work. 10. The Champion family is starting a cell phone plan. They have two plan options as shown in the chart below. Plan Option A Monthly Fee $24 Price Per Minute $ .30 B $16 $ .55 a. Write an equation that shows the cost per person for each option. b. Solve the system of equations. c. Find the number of minutes for which the total cost is the same with both plan options. 2