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Sample Problem 1 Solve the following linear systems using row reduction. State whether the system has no solution, a unique solution, or infinitely many solutions. a. 3x 2 y 6 2 x 3 y 6 b. 2 x1 x2 x3 4 3x1 x2 x3 5 c. ab 0 3a b 2 a b 1 d. 2x 4 y 7 0 3x 6 y 5 0 Sample Problem 2 One serving of cereal contains 60 calories and 11 grams of carbohydrates. One serving of juice contains 80 calories and 21 grams of carbohydrates. If you wish to follow a strict diet that only allows an intake of exactly 200 calories and 43 grams of carbohydrates, how many servings of cereal and juice should you eat? Sample Problem 3 In your pickle jar you have a collection of 140 coins consisting of nickels, dimes and quarters. After carefully counting all these coins you get a total of $10.00. In addition, you notice that there are twice as many dimes as there are quarters. How many nickels, dimes and quarters do you have? Using the number of nickels, dimes and quarters in the collection as variables, set up a 3 3 linear system and solve it. Sample Problem 4 In 2000, total revenues from sales of recorded rock, rap and classical music amounted to $5.8 billion. Rock music brought in twice as much revenue as rap music and 9 times as much revenue as classical music. How much revenue was earned in 2000 in each of the three music categories?