5. Can you explain whether there can be only one method to solve a linear system of equations? If yes, give an example of such a system of equations. if not, explain why not. Algebraic For the following exercises. determine whether the ordered triple given is the solution to the system of equations. For the following exercises, solve each system by elimination. 3x-47 + 22 = =15 2xx + 4 + 2=16 2x + 3y + 5z = 20 5x 27 + 32- 20 42 2* 4 32 - 90 x + 6x 8:-21 5x + 2+ + 42 - 0 13. -3x + 2y + z = 10 4x-3y + 5z =-3 4x-3y + 5z = 31 14. * + 2, + +2-20 X+jy-22 = =29 5x-2) + 32 =4For the following exercises, solve each system by Gaussian elimination. 2x - y + 3z = 17 17. -5x + 4y-2z = -46 2y + 5z = -7 5x-6y + 3z = 50 10. +4y = 10 2x =10 2xx + 3 68 -1 19. -4x-by + 122 - * + 21 5= =10 4x + 0y-ZZ = 8 20. 6x + 9 32 -12 2x + 3x 42-5 21. -3x + 2y + z = 11 -x + 5y + 3z =4 10x + 2y-14z = 8 22. =x-2 4 - -12x-61 + 67 - -12 23. 2y + 3z = -14 -16y-24z = -112 5x-3y + 4z = -1x+y+z=0 25. 2x - y + 3z = 0 X - Z=0 3x + 2y-5z = 6 20. 5x-4 +32 =-12 4x + Jy-2z = 15 2. 2x 3 32-0 * 28. 4x - x+5y 2 6x-5y + 6z = 38 29. =x - Sy+$z=1 -4x - By - z =-74 5x - zy+-z= _13 10 30. 7 5 20 3,X + Z =1 33. + 1 Z= -8 X + Z= -5 y + Z 34. W N WE 7 23 Z= 3 oo| un y+ Z X +37=-5 35. 55 3 3 80 TOO 36. 2 3 4 Z 3 3 to 0.1x-0.2y + 0.3z = 2 37. 0.5x-0.1y + 0.4z = 8 0.7x-0.2y + 0.3z = 8 1 0.19 0.32 - 0.2 38 08x 1 049 12: -Q.10.1x + 0.2y + 0.3z = 0.37 41. 0.1x-0.2y-0.3z = -0.27 0.5x-0.1y-0.3z = -0.03 0.5x 0.5 0.32 = 0.13 42 04x O.ly 0.32 _ 0.11 0.2x 0.8 0.9 - 0.32 05x +02 -037 -1 43 0.4x 0.6+ 1 072 -0.8 0.3x 0. 1 0.92 06 0.3x + 0.3, + 0.52 - 0.6 44. 0.4x + 0.4 + 0.42 - 1.8 Q4 * + 02+ 10.15 -15 0.8x + 0.8y + 0.8z = 2.4 45. 0.3x-0.5y + 0.2z = 0 0.1x + 0.2y + 0.3z = 0.6For the following exercises, solve the system for x, y, and z. *H2 3 x-1 y-3 46. z+1 2 2 2 z-3 3 5x 3+ z+1 2 47 6x+ 1-9 2+27 - -3 6 3 48 x-2 y+1 z+8 4 8 12 x+6 2+4 3 3 3 2 x-3 1+2 Z-3 2 49. *+2 + y-5 4 2 + 2+4 2 = 1 x+6 y-3 2 7+z+1=9 x-1 + 143 4 + 2+2 = 1 6 50. 4x + 3y=2z =11 0.02xx + 0.015 0.0120.06553. At a family reunion, there were only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and grandparents were in attendance? 54. An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many of each animal are at the shelter? 55. Your roommate, Sarah, offered to buy groceries for you and your other roommate. The total bill was $82. She forgot to save the individual receipts but remembered that your groceries were $0.05 cheaper than half of her groceries, and that your other roommate's groceries were $2.10 more than your groceries. How much was each of your share of the groceries? 56. Your roommate, John, offered to buy household supplies for you and your other roommate. You live near the border of three states, each of which has a different sales tax. The total amount of money spent was $100.75. Your supplies were bought with 5% tax, John's with 8% tax, and your third roommate's with 9% sales tax. The total amount of money spent without taxes is $93.50. If your supplies before tax were $1 more than half of what your third roommate's supplies were before tax, how much did each of you spend? Give your answer both with and without taxes. 57. Three coworkers work for the same employer. Their jobs are warehouse manager, office manager, and truck driver. The sum of the annual salaries of the warehouse manager and office manager is $82,000. The office manager makes $4,000 more than the truck driver annually. The annual salaries of the warehouse manager and the truck driver total $78,000. What is the annual salary of each of the co-workers?69. At one time, in the United States, 398 species of animals were on the endangered species list. The top groups were mammals, birds, and fish, which comprised 55% of the endangered species. Birds accounted for 0.7% more than fish, and fish accounted for 1.5% more than mammals. What percent of the endangered species came from mammals, birds, and fish?61. Last year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one could purchase all three cars for a total of $140,000. This year, due to inflation, the same cars would cost $151,830. The cost of the BMW increased by 8%, the Jeep by 5%, and the Toyota by 12%. If the price of last year's Jeep was $7,000 less than the price of last year's BMW, what was the price of each of the three cars last year? 62. A recent college graduate took advantage of his business education and invested in three investments immediately after graduating. He invested $80,500 into three accounts, one that paid 4% simple interest, one that paid 35% simple interest, and one that paid 2-% simple interest. He earned $2,670 interest at the end of one year. If the amount of the money invested in the second account was four times the amount invested in the third account, how much was invested in each account? 63. You inherit one million dollars. You triwest it all in three accounts for one year. The first account pays 3% compounded annually, the second account pays 4% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $34,800 in interest. If you invest four times the money into the account that pays 3% compared to 26, how much did you invest in each account? 64. You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 3% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $3,650 in interest. If you invest five times the money in the account that pays 4% compared to 3%, how much did you invest in each account? 65. The top three countries in oil consumption in a certain year are as follows: the United States, Japan, and China. In millions of barrels per day, the three top countries consumed 39.8% of the world's consumed oil. The United States consumed 0.7% more than four times China's consumption. The United States consumed 5% more than triple Japan's consumption. What percent of the world oil consumption did the United States, Japan, and China consume?1