Lesson 6-1: Graphing Sstems of Equations Date: Eample 1: Use the graph to determine whether each sstem is consistent or inconsistent and if it is independent or dependent. a. = 1 and = + 1 b. = 1 and = + 2 c. = 1 and 3 + 3 = 3 Eample 2: Graph the sstem of equations. Then determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it. A. = 2 + 3 and 8 4 = 12 Page1
Eample 2: Graph the sstem of equations. Then determine whether the sstem has no solution, one solution, or infinitel man solutions. If the sstem has one solution, name it. B. = 2 and 3 + 2 = 9 Eample 3: Natalie rode 20 miles last week and plans to ride 35 miles per week. Dan rode 50 miles last week and plans to ride 25 miles per week. Predict the week in which Natalie and Dan will have ridden the same number of miles. Step 1: Write an equation for the number of miles Natalie rides her bike. Step 2: Write an equation for the number of miles Dan rides his bike. Step 3: Graph both equations. Step 4: Estimate the point at which the graphs intersect. Page2
Lesson 6-2: Substitution Date: Eample 1: Use substitution to solve the sstem of equations. 2 = 3 3 + 5 = 24 Eample 2: Solve the sstem of equations twice using the substitution method. Page3
Eample 3: Use substitution to solve the sstem of equations. 2 + 2 = 8 + = 2 Eample 4: A nature center charges $35.25 for a earl membership and $6.25 for a single admission. Last week it sold a combined total of 50 earl memberships and single admissions for $660.50. How man memberships and how man single admissions were sold? Page4
Lesson 6-3: Elimination Using Addition and Subtraction Date: Eample 1: Use elimination to solve the sstem of equations. 3 + 4 = 12 3 6 = 18 Eample 2: Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. Page5
Eample 3: Use elimination to solve the sstem of equations. 4 + 2 = 28 4 3 = 18 Eample 4: A hardware store earned $956.50 from renting ladders and power tools last week. The store charged 36 das for ladders and 85 das for power tools. This week the store charged 36 das for ladders, 70 das for power tools, and earned $829. How much does the store charge per da for ladders and for power tools? Page6
Lesson 6-4: Elimination Using Multiplication Date: Eample 1: Use elimination to solve the sstem of equations. 2 + = 23 3 + 2 = 37 Eample 2: Use elimination to solve the sstem of equations. 4 + 3 = 8 3 5 = 23 Page7
Eample 3: A fishing boat travels 10 miles downstream in 30 minutes. The return trip takes the boat 40 minutes. Find the rate in miles per hour of the boat in still water. Let b = Let c = Down-stream Return r t d d = rt Page8
Lesson 6-5: Appling Sstems of Linear Equations Date: Eample 1: Determine the best method to solve the sstem of equations. Then solve the sstem. A. 2 + 3 = 23 4 + 2 = 34 B. At the school pool part, Mr. Lewis bought 1 adult ticket and 2 child tickets for $10. Mrs. Vroom bought 2 adult tickets and 3 child tickets for $17. Determine the best method to solve the sstem of equations. Then solve the sstem. Page9
Eample2: A. Ace Car Rental rents a car for $45 and $0.25 per mile. Star Car Rental rents a car for $35 and $0.30 per mile. How man miles would a driver need to drive before the cost of renting a car at Ace Car Rental and renting a car at Star Car Rental were the same? B. The cost to rent a video game from Action Video is $2 plus $0.50 per da. The cost to rent a video game at TeeVee Rentals is $1 plus $0.75 per da. After how man das will the cost of renting a video game at Action Video be the same as the cost of renting a video game at TeeVee Rentals? Page10
Lesson 6-6: Sstems of Inequalities Date: Eample 1: Solve the sstem of inequalities b graphing. A. < 2 + 2 3 B. 2 + 4 + 2 > 4 Page11
Eample 2: Solve the sstem of inequalities b graphing. 3 + 1 3 + 2 Eample 3: A. SERVICE A college service organization requires that its members maintain at least a 3.0 grade point average, and volunteer at least 10 hours a week. Define the variables and write a sstem of inequalities to represent this situation. Then graph the sstem. B. Name one possible solution. C. Is (3.5, 8) a solution? Page12