4.2 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Mixed Exercises: Objectives 1 and 3 1) If you were asked to solve this system by substitution, why would it be easiest to begin by solving for y in the fi rst equation? 7x y 1 2x 5y 9 It is the only variable with a coeffi cient of 1. 2) When is the best time to use substitution to solve a system? when one of the variables has a coeffi cient of 1 or 1 3) When solving a system of linear equations, how do you know whether the system has no solution? The variables are eliminated, and you get a false statement. 4) When solving a system of linear equations, how do you know whether the system has an infi nite number of solutions? The variables are eliminated, and you get a true statement. Solve each system by substitution. 5) y 4x 3 6) y 3x 10 5x y 15 (2, 5) 5x 2y 14 (6, 8) 7) x 7y 11 8) x 9 y 4x 5y 2 (3, 2) 3x 4y 8 (4, 5) 9) x 2y 3 10) x 4y 1 4x 5y 6 (1, 2) 5x 3y 5 (1, 0) 11) 2y 7x 14 12) 2x y 3 4x y 7 (0, 7) 3x 2y 3 (3, 3) 13) 9y 18x 5 14) 2x 30y 9 2x y 3 x 6 15y 15) x 2y 10 16) 6x y 6 3x 6y 30 12x 2y 12 17) 10x y 5 18) 2y x 4 5x 2y 10 x 6y 8 19) x 4 5 , 3b a b 3 5 y 7 20) y 3 2 x 5 a1, 3 2 x 4y 24 (4, 5) 2x y 5 (0, 5) 21) 4y 2x 4 22) 3x y 12 2y x 2 6x 10 2y 23) 2x 3y 6 24) 2x 5y 4 5x 2y 7 (3, 4) 8x 9y 6 (3, 2) 25) 6x 7y 4 26) 4x 6y 13 9x 2y 11 7x 4y 1 5 a a1, b 3 3 2 , 2b 27) 18x 6y 66 28) 6y 15x 12 12x 4y 19 5x 2y 4 Objective 2: Solve a System Containing Fractions or Decimals 29) If an equation in a system contains fractions, what should you do fi rst to make the system easier to solve? Multiply the equation by the LCD of the fractions to eliminate the fractions. 30) If an equation in a system contains decimals, what should you do fi rst to make the system easier to solve? Multiply the equation by the power of 10 that will eliminate the decimals. Solve each system by substitution. 1 4 x 31) 1 2 y 1 32) 2 9 x 2 9 y 2 2 3 x 1 6 y 25 6 (6, 1) 7 4 x 1 8 y 3 4 (1, 8) 1 6 x 33) 4 3 y 13 3 34) 1 10 x 1 2 y 1 5 2 5 x 3 2 y 18 5 (6, 4) 1 3 x 1 2 y 3 2 (3, 1) x 10 35) y 2 13 10 36) x 3 y 2 5 3 x 3 5 4 y 3 2 (3, 2) x 5 4 5 y 1 (5, 0) 37) y 5 2 x 2 38) 2 15 x 1 3 y 2 3 3 4 x 3 10 y 3 5 2 3 x 5 3 y 1 2 39) 3 4 x 1 2 y 6 40) 5 3 x 4 3 y 4 3 x 3y 8 (8, 0) y 2x 4 (4, 4) 41) 0.2x 0.1y 0.1 42) 0.01x 0.09y 0.5 0.01x 0.04y 0.23 0.02x 0.05y 0.38 (3, 5) (4, 6) 43) 0.6x 0.1y 1 44) 0.8x 0.7y 1.7 0.4x 0.5y 1.1 0.6x 0.1y 0.6 (1.5, 1) (0.5, 3) 45) 0.02x 0.01y 0.44 46) 0.3x 0.1y 3 0.1x 0.2y 4 0.01x 0.05y 0.06 (16, 12) (9, 3) 47) 2.8x 0.7y 0.1 48) 0.1x 0.3y 1.2 0.04x 0.01y 0.06 1.5y 0.5x 6 260 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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