Solutions to Try Its
1. Not a solution.
2. The solution to the system is the ordered pair [latex]\left(-5,3\right)[/latex].
3. [latex]\left(-2,-5\right)[/latex]
4. [latex]\left(-6,-2\right)[/latex]
5. [latex]\left(10,-4\right)[/latex]
6. No solution. It is an inconsistent system.
7. The system is dependent so there are infinite solutions of the form [latex]\left(x,2x+5\right)[/latex].
8. 700 children, 950 adults
Solutions to Odd-Numbered Exercises
1. No, you can either have zero, one, or infinitely many. Examine graphs.
3. This means there is no realistic break-even point. By the time the company produces one unit they are already making profit.
5. You can solve by substitution (isolating [latex]x[/latex] or [latex]y[/latex] ), graphically, or by addition.
7. Yes
9. Yes
11. [latex]\left(-1,2\right)[/latex]
13. [latex]\left(-3,1\right)[/latex]
15. [latex]\left(-\frac{3}{5},0\right)[/latex]
17. No solutions exist.
19. [latex]\left(\frac{72}{5},\frac{132}{5}\right)[/latex]
21. [latex]\left(6,-6\right)[/latex]
23. [latex]\left(-\frac{1}{2},\frac{1}{10}\right)[/latex]
25. No solutions exist.
27. [latex]\left(-\frac{1}{5},\frac{2}{3}\right)[/latex]
29. [latex]\left(x,\frac{x+3}{2}\right)[/latex]
31. [latex]\left(-4,4\right)[/latex]
33. [latex]\left(\frac{1}{2},\frac{1}{8}\right)[/latex]
35. [latex]\left(\frac{1}{6},0\right)[/latex]
37. [latex]\left(x,2\left(7x - 6\right)\right)[/latex]
39. [latex]\left(-\frac{5}{6},\frac{4}{3}\right)[/latex]
41. Consistent with one solution
43. Consistent with one solution
45. Dependent with infinitely many solutions
47. [latex]\left(-3.08,4.91\right)[/latex]
49. [latex]\left(-1.52,2.29\right)[/latex]
51. [latex]\left(\frac{A+B}{2},\frac{A-B}{2}\right)[/latex]
53. [latex]\left(\frac{-1}{A-B},\frac{A}{A-B}\right)[/latex]
55. [latex]\left(\frac{CE-BF}{BD-AE},\frac{AF-CD}{BD-AE}\right)[/latex]
57. They never turn a profit.
59. [latex]\left(1,250,100,000\right)[/latex]
61. The numbers are 7.5 and 20.5.
63. 24,000
65. 790 sophomores, 805 freshman
67. 56 men, 74 women
69. 10 gallons of 10% solution, 15 gallons of 60% solution
71. Swan Peak: $750,000, Riverside: $350,000
73. $12,500 in the first account, $10,500 in the second account.
75. High-tops: 45, Low-tops: 15
77. Infinitely many solutions. We need more information.