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].
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.Licenses & Attributions
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- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution.
