Warm up

Solve the given system by substitution:

1) 2x – y = 7

3x + 3y = - 3

Solve the given system by elimination:

2) -3x + 4y = -4

3x – 6y = 6

1)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.

2)Elimination: Can be applied to any system, but it is especially convenient when a variable appears in different equations with coefficients that are opposites.

3)Graphing: Can provide a useful method for estimating a solution.

1. y = 4x – 35x – 2y = 6

2. 4x – 5y = 132x + 5y = 5

13. 3

22 1

y x

y x

5. 3x – 2y = 6y = 2x – 4

6. x + y = 42x + 3y = 7

24. 2

31

y x

y x

1. Define all variables.2. Write the system of equations.3. Solve using best method &

showing all steps.4. State your solution in

sentence form.5. Check your solution.

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:

 

System of equations:

State your solution(s):

Solve

S = # of Student TicketsG = # of General Admin Tickets

S + G = 3503S + 5G = 1450

G = 200S = 150

I sold 200 general admission tickets and 150 student tickets.

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?

Define variables:

 

System of equations:

State your solution(s):

Solve

S = # of ShirtsP = # of Pants

S + P = 26

125S + 225G = 4950

P = 17

S = 9Missy bought 17 pairs of pants and 9 shirts.

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?

Define variables:

 

System of equations:

State your solution(s):

Solve

B = price of a bag of balloonsS = price of a bag of stars

6B + 5S = 19.208B + 2S = 15.80

B = 1.45S = 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. 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?

Define variables:

 

System of equations:

State your solution(s):

Solve

D = cost of DVDC = cost of CD

3D + 2C = 425D + C = 56 D = 10

C = 6A DVD cost $10 and a CD costs $6.

Worksheet