Test Tomorrow 2nd block

elimination or substitution

100

x+3y=7

-x+y=1

x=1 and y=2

200

y = −2

4x − 3y = 18

x=3 and y=-2

300

−4x + y = 6

−5x − y = 21

x=-3 and x=-6

400

6x + 6y = −6

5x + y = −13

x=-3 and y=2

500

−2x + 6y = 6

−7x + 8y = −5

x=3 and y=2

square roots

100

x²=4

x=2 and x=-2

200

x²-49 = 0

x=7 and x=-7

300

2x²-128=0

x=8 and x=-8

400

3x²-520=-13

x=13 and x=-13

500

6x²-340 -2x²=-16

x=9 and x=-9

add/subtract polynomials

100

Subtract the polynomials 

(2x + 15) - (x + 4)

x + 11

200

Add the polynomials

(3x⁴ + 6x² + 14x - 5) + (3x³ + 3x² - 10)

2x2 +8x + 8

300

Subtract the polynomials 

(-7x² - 4x - 7) - (7x² - 4x - 11)

-14x² + 4

400

Add the polynomials

(-3x³ + x² - 3x⁴ + x -6) + (5x⁴+3x³+2x² - 2x + 15)

2x⁴+3x³-x+9

500

Subtract the polynomials

(3x - 3x² - 3x³ - 3x⁴) - (3x - 3x² - 3x³ - 3x⁴)

0

factoring quadratics

100

Factor  x²+8x+12 into two expressions

(x+6)(x+2)

200

Factor  x²+20x+19 into two expressions

(x+1)(x+19)

300

Factor  x²-5x+14 into two expressions

(x-7)(x+2)

400

Factor  x²-16x+17 into two expressions

(x-17)(x+1)

500

Factor  x²-x-72 into two expressions

(x-9)(x+8)

real-world systems

100

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

200

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

300

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

400

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

500

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