elimination or substitution
x+3y=7
-x+y=1
x=1 and y=2
x2=4
x=2 and x=-2
Subtract the polynomials
(2x + 15) - (x + 4)
x + 11
Factor x2+8x+12 into two expressions
(x+6)(x+2)
You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. How many hotdogs and soda did you sell?
35 hotdogs and 52 sodas
y = −2
4x − 3y = 18
x=3 and y=-2
x2-49 = 0
x=7 and x=-7
Add the polynomials
(3x4 + 6x2 + 14x - 5) + (3x3 + 3x2 - 10)
2x2 +8x + 8
Factor x2+20x+19 into two expressions
(x+1)(x+19)
A youth group and their leaders visited Mammoth Cave. Two adults and 5 students in one van
paid $77 for the Grand Avenue Tour of the cave. Two adults and 7 students in a second van paid
$95 for the same tour. Find the adult price and the student price of the tour.
16 adults and 9 students
−4x + y = 6
−5x − y = 21
x=-3 and x=-6
2x2-128=0
x=8 and x=-8
Subtract the polynomials
(-7x2 - 4x - 7) - (7x2 - 4x - 11)
-14x2 + 4
Factor x2-5x+14 into two expressions
(x-7)(x+2)
The owners of the River View Restaurant have hired enough servers to handle 17 tables of
customers, and the fire marshal has approved the restaurant for a limit of 56 customers. How many
two-seat tables and how many four-seat tables should the owners purchase?
Two-Seated = 6; Four-Seated = 11
6x + 6y = −6
5x + y = −13
x=-3 and y=2
3x2-520=-13
x=13 and x=-13
Add the polynomials
(-3x3 + x2 - 3x4 + x -6) + (5x4+3x3+2x2 - 2x + 15)
2x4+3x3-x+9
Factor x2-16x+17 into two expressions
(x-17)(x+1)
The manager of a movie theater found that Saturday’s sales were $3675. He
knew that a total of 650 tickets were sold Saturday. Adult tickets cost $7.50, and
children’s tickets cost $4.50. How many of each kind of ticket were sold?
Adults = 250 tickets; Students = 400 tickets
−2x + 6y = 6
−7x + 8y = −5
x=3 and y=2
6x2-340 -2x2=-16
x=9 and x=-9
Subtract the polynomials
(3x - 3x2 - 3x3 - 3x4) - (3x - 3x2 - 3x3 - 3x4)
0
Factor x2-x-72 into two expressions
(x-9)(x+8)
A birding club holds an annual photography contest among its members. After a set time limit in
a particular park, contestants receive 4 points for photos of songbirds and 20 points for photos of
birds of prey. Last year’s winner had a total of 200 points from 38 photos of individual birds. How
many of each type of bird did the winner photograph?
Songbirds = 35; Birds of Prey = 3