4.1 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Objective 1: Determine Whether an Ordered Pair Is a Solution of a System Determine whether the ordered pair is a solution of the system of equations. 1) x 2y 6 2) y x 4 x 3y 13 x 3y 8 (8, 7) yes (1, 3) yes 3) 5x y 21 4) 7x 2y 14 2x 3y 11 5x 6y 12 (4, 1) no (2, 0) no 5) 5y 4x 5 6) x 9y 7 6x 2y 21 18y 7x 4 a 5 2 , 3b yes a1, 2 3 b no 7) y x 11 8) x y x 5y 2 y 5 8 x 13 (0, 9) no (8, 8) yes Mixed Exercises: Objectives 2 and 3 9) If you are solving a system of equations by graphing, how do you know whether the system has no solution? The lines are parallel. 10) If you are solving a system of equations by graphing, how do you know whether the system has an infi nite number of solutions? The graphs are the same line. Solve each system of equations by graphing. If the system is inconsistent or the equations are dependent, identify this. 11) y 2 3 x 3 12) y 1 2 x 2 y x 2 y 2x 1 13) y x 1 14) y 2x 3 y 1 2 x 4 y x 3 15) x y 1 16) 2x 3y 6 x 2y 14 x y 7 17) x 2y 7 18) x 2y 4 3x y 1 3x 4y 12 3 4 x y 0 20) y x 19) 3x 4y 20 4x 4y 2 21) y 1 3 x 2 22) 5x 5y 5 4x 12y 24 x y 1 23) x 8 4y 24) x y 0 3x 2y 4 7x 3y 12 25) y 3x 1 26) 2x y 1 12x 4y 4 2x y 3 27) x y 0 28) x 2 y 1 2 x 3 y 5 2 x 1 29) 3x y 4 30) 5x 2y 6 y 1 15x 6y 18 31) y 3 5 x 6 32) y x 2 3x 5y 10 2x y 5 Write a system of equations so that the given ordered pair is a solution of the system. For 33–38, answers may vary. 33) (2, 5) 34) (3, 1) 35) (4, 3) 36) (6, 1) 37) a 1 3 , 4b 38) a0, 3 2 b For Exercises 39–42, determine which ordered pair could be a solution to the system of equations that is graphed. Explain why you chose that ordered pair. 39) x y A. (2, 6) B. (3, 4) C. (3, 4) D. (2, 3) C; (3, 4) is in quadrant II. 40) x y A. a7 2 , 1 2 b B. (4, 1) C. a9 4 , 3 4 b D. a 10 3 , A; a7 2 3 b 2 , 1 2 b is in quadrant IV. 252 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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