935 9.5 Nonlinear Systems of Equations 14. In Example 5, there were four solutions to the system, but there were no points of intersection of the graphs. If a nonlinear system has nonreal complex numbers as components of its solutions, will they appear as intersection points of the graphs? Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5. 15. x2 - y = 0 x + y = 2 16. x2 + y = 2 x - y = 0 17. y = x2 - 2x + 1 x - 3y = -1 18. y = x2 + 6x + 9 x + 2y = -2 19. y = x2 + 4x 2x - y = -8 20. y = 6x + x2 4x - y = -3 21. 3x2 + 2y2 = 5 x - y = -2 22. x2 + y2 = 5 -3x + 4y = 2 23. x2 + y2 = 8 x2 - y2 = 0 24. x2 + y2 = 10 2x2 - y2 = 17 25. 5x2 - y2 = 0 3x2 + 4y2 = 0 26. x2 + y2 = 0 2x2 - 3y2 = 0 27. 3x2 + y2 = 3 4x2 + 5y2 = 26 28. x2 + 2y2 = 9 x2 + y2 = 25 29. 2x2 + 3y2 = 5 3x2 - 4y2 = -1 30. 3x2 + 5y2 = 17 2x2 - 3y2 = 5 31. 2x2 + 2y2 = 20 4x2 + 4y2 = 30 32. x2 + y2 = 4 5x2 + 5y2 = 28 33. 2x2 - 3y2 = 12 6x2 + 5y2 = 36 34. 5x2 - 2y2 = 25 10x2 + y2 = 50 35. xy = -15 4x + 3y = 3 36. xy = 8 3x + 2y = -16 37. 2xy + 1 = 0 x + 16y = 2 38. -5xy + 2 = 0 x - 15y = 5 39. 3x2 - y2 = 11 xy = 12 40. 5x2 - 2y2 = 6 xy = 2 41. x2 - xy + y2 = 5 2x2 + xy - y2 = 10 42. 3x2 + 2xy - y2 = 9 x2 - xy + y2 = 9 43. x2 + 2xy - y2 = 14 x2 - y2 = -16 44. x2 + 3xy - y2 = 12 x2 - y2 = -12 45. x2 + y2 = 25 x - y = 5 46. x2 + y2 = 9 x + y = 3 47. x = y x2 + y2 = 18 48. 2x + y = 4 x2 + y2 = 5 49. 2x2 - y2 = 4 x = y 50. x2 + y2 = 9 x = y Many nonlinear systems cannot be solved algebraically, so graphical analysis is the only way to determine the solutions of such systems. Use a graphing calculator to solve each nonlinear system. Give x- and y-coordinates to the nearest hundredth. 51. y = log1x + 52 y = x2 52. y = 5x xy = 1 53. y = ex+1 2x + y = 3 54. y = 23 x - 4 x2 + y2 = 6 Solve each problem using a system of equations in two variables. See Example 6. 55. Unknown Numbers Find two numbers whose sum is -17 and whose product is 42. 56. Unknown Numbers Find two numbers whose sum is -10 and whose squares differ by 20. 57. Unknown Numbers Find two numbers whose squares have a sum of 100 and a difference of 28. 58. Unknown Numbers Find two numbers whose squares have a sum of 194 and a difference of 144. 59. Unknown Numbers Find two numbers whose ratio is 9 to 2 and whose product is 162.
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