1) Determine whether a 2 3 , 4b is a solution of the system 9x 5y 14 yes 6x y 0. Solve each system by graphing. 2) y x 2 3) 3y 6x 6 3x 4y 20 (4, 2) 2x y 1 4) The graph shows the unemployment rate in the civilian labor force in Vermont and Virginia in the month of September for 2008 to 2011. (www.bls.gov) Unemployment Rate in September 7.0 6.5 6.0 5.5 5.0 4.5 Virginia 2008 2009 2010 2011 Year 4.0 Rate (as a percent) Vermont a) When were more people unemployed in Vermont? Approximately what percent of the state’s population was unemployed at that time? 2008; Approximately 5.2% of the population was unemployed. b) Write the point of intersection of the graphs as an ordered pair in the form (year, percentage) and explain its meaning. (2009, 6.7); In 2009, 6.7% of the population of Vermont and Virginia were unemployed. c) Which line segment has the most positive slope? How can this be explained in the context of the problem? Solve each system by the substitution method. 5) 3x 10y 10 x 8y 9 6) y 1 2 x 3 4x 8y 24 a5, 1 2 b infi nite number of solutions of the form e (x, y) ` y 1 2 x 3 f Solve each system by the elimination method. 7) 2x 5y 11 (3, 1) 7x 5y 16 8) 3x 4y 24 (0, 6) 7x 3y 18 9) 6x 9y 14 4x 6y 5 Solve each system using any method. 10) 11x y 14 (2, 8) 9x 7y 38 11) 5 8 x 1 4 y 1 4 1 3 x 1 2 y 4 3 (2, 4) 12) 7 4(2x 3) x 7 y 4 a , 0b 5(x y) 20 8(2 x) x 12 3 13) Write a system of equations in two variables that has (5, 1) as its only solution. Answers may vary. Write a system of equations, and solve. 14) The area of Yellowstone National Park is about 1.1 million fewer acres than the area of Death Valley National Park. If they cover a total of 5.5 million acres, how big is each park? (www.nps.gov) Yellowstone: 2.2 mil acres; Death Valley: 3.3 mil acres 15) The Mahmood and Kuchar families take their kids to an amusement park. The Mahmoods buy one adult ticket and two children’s tickets for $85.00. The Kuchars spend $150.00 on two adult and three children’s tickets. How much did they pay for each type of ticket? adult: $45.00; child: $20.00 16) The width of a rectangle is half its length. Find the dimensions of the rectangle if the perimeter is 114 cm. 17) How many milliliters of a 12% alcohol solution and how many milliliters of a 30% alcohol solution must be mixed to obtain 72 mL of a 20% alcohol solution? 18) Rory and Lorelai leave Stars Hollow, Connecticut, and travel in opposite directions. Rory drives 4 mph faster than Lorelai, and after 1.5 hr they are 120 miles apart. How fast was each driving? Rory: 42 mph; Lorelai: 38 mph Graph each inequality. 19) y 3x 1 20) x 4y 12 Graph the solution set of each system of inequalities. 21) x 3 22) 2x y 1 y 1 2 x 1 x y 0 length: 38 cm; width: 19 cm 12%: 40 mL; 30%: 32 mL Chapter 4: Test *Additional answers can be found in the Answers to Exercises appendix. www.mhhe.com/messersmith CHAPTER 4 Test 305
messersmith_power_introductory_algebra_1e_ch4_7_10
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