252 Chapter 3 Systems of Linear Equations and Inequalities Concept 2: Solving Inconsistent Systems and Systems of Dependent Equations For Exercises 23–30, solve the system using the substitution method. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. (See Examples 3–4.) 23. 24. 25. 26. 27. 28. 29. 30. x 4y 1 12y 3x 3 y 31. When using the substitution method, explain how to determine whether two linear equations in a system are dependent. 32. When using the substitution method, explain how to determine whether a system of linear equations is inconsistent. Mixed Exercises For Exercises 33–56, solve the system using the substitution method. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. 33. 34. 35. 36. 37. 38. x 2x y 4 8x y 8 1 5 39. 40. 41. 3x 2y 6 x 4y 4 300x 125y 1350 y x 3 y x 1 y 2 8 42. 43. 44. 200y 150x 2x y 6 x 4y 8 45. 46. 47. y 3.1x 63.1 y 4.1x 56.8 48. 49. 21x 2y2 50. 5x 2y 25 2x y 6 12 6x 13y 12 4x 4y 5 x 4y 5 2 y 2.7x 5.1 y 6.8x 2.3 1 16 x 1 4 y 1 2 1 6 x 1 12 y 1 2 y 4 1 1 3 x 1 24 y 1 2 1 4 x 1 8 y 1 y x 4 21 5 1 6 y 5 3 x 1 4 y 17 4 y 1.2x 4.6 1.1x y 9.6 y 2 3 x 1 3 x 1.3y 1.5 y 0.8x 1.8 6x 5y 8 10x 31y 102 3x y 7 14 6x 2y x 4y 8 3x 3 12y 5x y 10 2y 10x 5 x 3 2 y 1 2 4x 6y 7 1 7 x 3 x 7y 4 2x 4y 22 x 2y 11 2x 6y 2 x 3y 1
miller_intermediate_algebra_4e_ch1_3
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