Solutions For Systems of Linear Equations: Two Variables

Solutions to Try Its

1. Not a solution.

2. The solution to the system is the ordered pair [latex]\left(-5,3\right)[/latex].

Two lines that cross at the point negative five, three. One line's equation is y equals four-fifths x plus 7. The other line's equation is y equals two-fifths x plus 5.

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.