(4.1) Determine whether the ordered pair is a solution of the system of equations. 1) x 5y 13 no 2) 8x 3y 16 yes 2x 7y 20 10x 6y 7 (4, 5) a3 2 , 4 3 b 3) If you are solving a system of equations by graphing, how do you know whether the system has no solution? The lines are parallel. Solve each system by graphing. 4) y 1 2 x 1 (2, 2) 5) x 3y 9 x y 4 x 3y 6 6) 6x 3y 12 7) x 2y 1 (3, 1) 2x y 4 2x 3y 9 Without graphing, determine whether each system has no solution, one solution, or an infinite number of solutions. 8) 8x 9y 2 9) y 5 2 x 3 x 4y 1 5x 2y 6 one solution infi nite number of solutions 10) The graph shows the number of millions of barrels of crude oil reserves in Alabama and Ohio from 2005 to 2009. (www.census.gov) 13) x 8y 19 (5, 3) 14) 12x 7y 9 4x 3y 11 8x y 6 (4.3) Solve each system using the elimination method. 15) x 7y 3 (4, 1) x 5y 1 16) 5x 4y 23 3x 8y 19 17) 10x 4y 8 5x 2y 4 18) 7x 4y 13 (3, 2) 6x 5y 8 Solve each system using the elimination method twice. 19) 2x 9y 6 5x y 3 20) 7x 4y 10 6x 3y 8 (4.2–4.3) 21) When is the best time to use substitution to solve a system? 22) If an equation in a system contains fractions, what should you do fi rst to make the system easier to solve? Solve each system by either the substitution or elimination method. 23) 6x y 8 9x 7y 1 24) 4y 5x 23 (1, 7) 2x 3y 23 1 3 x 25) 2 9 y 2 3 (0, 3) 5 12 x 1 3 y 1 26) 0.02x 0.01y 0.13 (10, 7) 0.1x 0.4y 1.8 27) 6(2x 3) y 4(x 3) 5(3x 4) 4y 11 3y 27x 28) x 3y 36 (9, 15) y 5 3 x 29) 3 4 x 5 4 y 7 8 4 2(x 5) y 3(1 2y) x 30) y 9 7 x 6 7 18x 14y 12 a 3 4 , 0b a5, 1 2 b infi nite number of solutions of the form {(x, y) 05x 2y 4} a33 43 , 36 43 b a62 45 , 4 45 b when one of the variables has a coeffi cient of 1 or 1 Multiply both sides of the equation by the LCD of the fractions to eliminate the fractions. a 5 3 , 2b a3 4 , 0b infi nite number of solutions of the form e (x, y) ` y 9 7 x 6 7 f Chapter 4: Review Exercises *Additional answers can be found in the Answers to Exercises appendix. Crude Oil Reserves 60 55 50 45 40 Ohio 2005 2006 2007 2008 2009 Year 35 Reserves (in millions of barrels) Alabama a) In 2006, approximately how much more crude oil did Ohio have in reserve than Alabama? about 4 million more barrels b) Write the point of intersection as an ordered pair in the form (year, reserves) and explain its meaning. c) Which line segment for Alabama has the most negative slope? How can this be explained in the context of the problem? (4.2) Solve each system by the substitution method. 11) 9x 2y 8 (2, 5) 12) y 6x 5 y 2x 1 12x 2y 10 www.mhhe.com/messersmith CHAPTER 4 Review Exercises 303
messersmith_power_introductory_algebra_1e_ch4_7_10
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