Download Systems Word Problems Notes

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.
“All I do is Solve”
http://www.schooltube.com/ch
annel/westervillesouthmath/
1. y = 4x – 3
5x – 2y = 6
2.
4x – 5y = 13
2x + 5y = 5
1
3. y  x  3
2
y  2 x  1
2
4. y  x  2
3
y  x 1
5. 3x – 2y = 6
y = 2x – 4
6. x + y = 4
2x + 3y = 7
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
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.
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:
S = # of Student Tickets
Solve
G = # of General Admin Tickets
System of equations:
S + G = 350
3S + 5G = 1450
State your solution(s):
I sold 200 general admission
tickets and 150 student
tickets.
G = 200
S = 150
Define variables:
Solve
S = # of Student Tickets
G = # of General Admin Tickets
System of equations:
S + G = 350
3S + 5G = 1450
State your solution(s):
I sold 200 general
admission tickets and
150 student tickets.
G = 200
S = 150
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:
Solve
S = # of Shirts
P = # of Pants
System of equations:
S + P = 26
125S + 225G = 4950
State your solution(s):
Missy bought 17 pairs
of pants and 9 shirts.
P = 17
S=9
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:
Solve
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
State your solution(s):
The price of the bag of
balloons is $1.45 and the
bag of stars is $2.10.
B = 1.45
S = 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:
Solve
D = cost of DVD
C = cost of CD
System of equations:
3D + 2C = 42
5D + C = 56
State your solution(s):
A DVD cost $10 and a
CD costs $6.
D = 10
C=6