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
Jan 23, 2016
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