Solve the given system by elimination: 2) -3x + 4y = -4 3x – 6y = 6 Warm up Solve the given system by substitution: 2x – y = 7 3x + 3y = - 3 Solve the given system by elimination: 2) -3x + 4y = -4 3x – 6y = 6

Summary of Methods Substitution: Requires that one of the variables be isolated on one side of the equation. It is especially convenient when one of the variables has a coefficient of 1 or -1. Elimination: Can be applied to any system, but it is especially convenient when a variable appears in different equations with coefficients that are opposites. Graphing: Can provide a useful method for estimating a solution.

Summary of Solving Systems by Westerville South H.S. “All I do is Solve” http://www.schooltube.com/channel/westervillesouthmath/

Best Method Graphing, Substitution, Elimination? 1. y = 4x – 3 5x – 2y = 6 2. 4x – 5y = 13 2x + 5y = 5

Best Method 5. 3x – 2y = 6 y = 2x – 4 6. x + y = 4 2x + 3y = 7

Solving Word Problems Using Systems

Steps Define all variables. Write the system of equations. Solve using best method & showing all steps. State your solution in sentence form. Check your solution.

G = 200 S = 150 Solve Define variables: 1. You are selling tickets for a high school basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450. How many of each type of ticket did you sell? Define variables: Solve S = # of Student Tickets G = # of General Admin Tickets G = 200 System of equations: S + G = 350 S = 150 3S + 5G = 1450 State your solution(s): I sold 200 general admission tickets and 150 student tickets.

Solve Define variables: S = # of Student Tickets G = # of General Admin Tickets System of equations: S + G = 350   3S + 5G = 1450 G = 200 State your solution(s): S = 150 I sold 200 general admission tickets and 150 student tickets.

2. Last Saturday Missy bought pants and shirts 2. Last Saturday Missy bought pants and shirts. Each shirt cost $125 and each pair of pants cost $225. She came home with 26 items and spent exactly $4950. How many pants and shirts did Missy buy?

Solve Define variables: S = # of Shirts P = # of Pants System of equations: S + P = 26   125S + 225G = 4950 P = 17 State your solution(s): S = 9 Missy bought 17 pairs of pants and 9 shirts.

3. You are in charge of decorating the gym for the Homecoming dance 3. You are in charge of decorating the gym for the Homecoming dance. You purchased 6 bags of balloons and 5 bags of large sparkling hanging stars all for $19.20. You soon realized that this was not enough to decorate the entire gym. On your second trip to the store, you bought 8 bags of balloons and 2 bags of large sparkling hanging stars all for $15.80. What was the price for each item?

Solve Define variables: B = price of a bag of balloons S = price of a bag of stars System of equations: 6B + 5S = 19.20   8B + 2S = 15.80 B = 1.45 State your solution(s): S = 2.10 The price of the bag of balloons is $1.45 and the bag of stars is $2.10.

4. Wally World had a sale on DVDs and CDs for Labor Day weekend 4. Wally World had a sale on DVDs and CDs for Labor Day weekend. Katie bought 3 DVDs and 2 CDs and spent $42. Emily bought 5 DVDs and 1 CD and spent $56. How much does each DVD and CD cost?

Solve Define variables: D = cost of DVD C = cost of CD System of equations: 3D + 2C = 42   5D + C = 56 D = 10 State your solution(s): C = 6 A DVD cost $10 and a CD costs $6.