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CPM Algebra I 2/2010 Chapter 6 Team Test Period_____ Name(s) ________________________ _______________________________________ CPM-Algebra English Sentences and Mathematical Sentences 1. Match each mathematical sentence on the left with its translation on the right. Then, for each mathematical sentence, declare what the variable “x” represents. ___a. 2x 8 22 x means_____________________ ___b. x 2(x 2) (x 2) 22 1. Rob’s number is equal to twice Bob’s number. Cob’s number is eight times larger than two less than Bob’s number. The sum of Rob’s number and Cob’s number is 22. 2. Jenna earned $22 by working 2 hours and receiving an $8 bonus. x means_____________________ ___c. 2x 8(x 2) 22 3. Toby’s cup can hold 8 times as many ounces of water as Terry’s. Together, the cups hold 22 ounces of water. x means_____________________ ___d. x 8x 22 x means_____________________ 4. A 22-ounce metal bracelet is created by mixing gold, silver, and zinc. There are two ounces less zinc than gold, and there is twice as much silver as zinc. Graphs of Systems of Equations 2. Use the graph at the right for each part. a. Write the rule/equation for each of the lines shown. ___________________ and ___________________ b. Solve the system algebraically. c. How does the graph help you know that your solution is correct? __________________________ __________________________________________________________________________ CPM Algebra I 2/2010 Guess & Check Format to help write Equations 3. You’ve decided to give your best friend a bag of marbles for his 15th birthday. Since you know that your friend likes red marbles better than brown ones, the number of red marbles in the bag is 4 fewer than 5 times the number of brown marbles. The bag contains 74 marbles. a. Solve using a Guess & Check table. Solution: _______________________________________ b. Use your Guess & Check table to help write an equation or system of equations to find out how many of each type of marble is in the bag. Variable(s) used: _______________________________________________ Equation(s): ___________________________________________________ c. Solve your equation/system of equations algebraically to answer the question Solution: _______________________________________ Methods for solving systems: Graph -- Equal Values -- Substitution -- Elimination Solve each system of equations for both variables. State your method and Show All Your Work!! 4. 5. 6. a+b=8 3a – 4b = 3 Chosen method: _____________________ x – 2y = 6 y = 11 – 3x Chosen method: _____________________ x = 2y + 4 x = 6y - 8 Chosen method: _____________________ Solution: ___________________________ Solution: ___________________________ Solution: ___________________________ CPM Algebra I 2/2010 Multiple Choice: _____7. Pearl’s work for solving this system of equations is shown here. All her work is correct. Which method is she using? System: y = –5 – x Pearl’s Solution: 2x + (–5 – x) = 20 2x + y = 20 x – 5 = 20 +5 +5 x = 25 A. Equal Values method y = -5 –(25) B. Substitution y = -30 C. Elimination D. Multiplication and then Elimination _____8. Edith is using substitution to solve the system of equations below. What should the first step be? y 3x 2x 8y 2 A. 2x 8(3x) 2 B. 3(2x 8y) 2 C. 2(3x) 8y 2 D. 3(2x 8x) 2 _____9. Mrs. Goolsby wants to use Elimination to solve the system of equations below. Choose the best first step. 3x y 5 2x 3y 10 A. Multiply the first equation by 2. B. Multiply the second equation by 3. C. Multiply the first equation by 3. D. Multiply the second equation by 2. CPM Algebra I 2/2010 10. Solve the following using substitution: X+2y=12 Y=2x+1 10____________________ 11. Solve using elimination: 3x+6y=6 4x-6y=8 11.____________________ 12. Sovle using any method you choose: X+2y=9 3x+2y=7 12.____________________ 13. Mr. Glass solved a system of equations using substitution and got the following result: 12= -4 a. What should he write as his final answer? b. What does this tell you about the graph of the sytem?