Solutions 29: Systems of Linear Equations: Two Variables
Solutions to Try Its
1. Not a solution.
2. The solution to the system is the ordered pair (−5,3).
3. (−2,−5)
4. (−6,−2)
5. (10,−4)
6. No solution. It is an inconsistent system.
7. The system is dependent so there are infinite solutions of the form (x,2x+5).
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 x or y ), graphically, or by addition.
7. Yes
9. Yes
11. (−1,2)
13. (−3,1)
15. (−53,0)
17. No solutions exist.
19. (572,5132)
21. (6,−6)
23. (−21,101)
25. No solutions exist.
27. (−51,32)
29. (x,2x+3)
31. (−4,4)
33. (21,81)
35. (61,0)
37. (x,2(7x−6))
39. (−65,34)
41. Consistent with one solution
43. Consistent with one solution
45. Dependent with infinitely many solutions
47. (−3.08,4.91)
49. (−1.52,2.29)
51. (2A+B,2A−B)
53. (A−B−1,A−BA)
55. (BD−AECE−BF,BD−AEAF−CD)
57. They never turn a profit.
59. (1,250,100,000)
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.