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Study Guides > Precalculus I

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)\left(-5,3\right). 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. (2,5)\left(-2,-5\right) 4. (6,2)\left(-6,-2\right) 5. (10,4)\left(10,-4\right) 6. No solution. It is an inconsistent system. 7. The system is dependent so there are infinite solutions of the form (x,2x+5)\left(x,2x+5\right). 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 xx or yy ), graphically, or by addition. 7. Yes 9. Yes 11. (1,2)\left(-1,2\right) 13. (3,1)\left(-3,1\right) 15. (35,0)\left(-\frac{3}{5},0\right) 17. No solutions exist. 19. (725,1325)\left(\frac{72}{5},\frac{132}{5}\right) 21. (6,6)\left(6,-6\right) 23. (12,110)\left(-\frac{1}{2},\frac{1}{10}\right) 25. No solutions exist. 27. (15,23)\left(-\frac{1}{5},\frac{2}{3}\right) 29. (x,x+32)\left(x,\frac{x+3}{2}\right) 31. (4,4)\left(-4,4\right) 33. (12,18)\left(\frac{1}{2},\frac{1}{8}\right) 35. (16,0)\left(\frac{1}{6},0\right) 37. (x,2(7x6))\left(x,2\left(7x - 6\right)\right) 39. (56,43)\left(-\frac{5}{6},\frac{4}{3}\right) 41. Consistent with one solution 43. Consistent with one solution 45. Dependent with infinitely many solutions 47. (3.08,4.91)\left(-3.08,4.91\right) 49. (1.52,2.29)\left(-1.52,2.29\right) 51. (A+B2,AB2)\left(\frac{A+B}{2},\frac{A-B}{2}\right) 53. (1AB,AAB)\left(\frac{-1}{A-B},\frac{A}{A-B}\right) 55. (CEBFBDAE,AFCDBDAE)\left(\frac{CE-BF}{BD-AE},\frac{AF-CD}{BD-AE}\right) 57. They never turn a profit. 59. (1,250,100,000)\left(1,250,100,000\right) 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.

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