Questões de Álgebra Linear e Inequações

31 Systems of Linear Equations with two variables Student Outcomes Students understand the possibility that there might be no real number solution to an equation or system of equations Students identify these situations and make the appropriate geometric connections Exercises 1 In the following exercises determine if the following points are solutions to the given system of equations a b 2 In the following exercises solve the following systems of equations by graphing a b c d c 3 After attending a major league baseball game the patrons often purchase souvenirs If a family purchases 5 tshirts a cap and 1 stuffed animal their total is 135 A couple buys 2 tshirts a cap and 3 stuffed animals for their nieces and spends 115 Another couple buys 2 tshirts a cap and 1 stuffed animal and their total is 85 What is the cost of each item 4 Write each system of linear equations as an augmented matrix a b 1 Write the system of equations that corresponds to the augmented matrix a 0 b 1 In the following exercise evaluate the determinant of the square matrix 0 1 In the following exercise find and then evaluate the indicated minors 35 Systems of Linear Inequalities Student Outcomes Students use systems of equations or inequalities to solve contextual problems and interpret solutions within a particular context Exercises 1 Find two numbers such that the sum of the first and three times the second is 6 and the sum of second and two times the first is 8 2 A chemist has two solutions a 40 methane solution and an 80 methane solution He wants 100 mL of a 70 methane solution How many mL of each solution does he need to mix 3 Pam has two part time jobs At one job she works as a cashier and makes 9 per hour At the second job she works as a tutor and makes 13 per hour One week she worked 30 hours and made 268 How many hours did she spend at each job 4 A store sells Brazilian coffee for 12 per lb and Columbian coffee for 14 per lb If the store decides to make a 150lb blend of the two and sell it for 11 per lb how much of each type of coffee should be used 5 A potter is making cups and plates It takes her 8 min to make a cup and 3 min to make a plate Each cup uses 3 4 lb of clay and each plate uses 1 lb of clay She has 20 hr available to make the cups and plates and has 250 lb of clay a What are the variables b Write inequalities for the constraints c Graph and shade the solution set d If she makes a profit of 2 on each cup and 150 on each plate how many of each should she make in order to maximize her profit e What is her maximum profit