Systems of Equations and Inequalities

Systems of Equations Graphically

100

What is the solution to this system of equations? 

(-2,1)

200

Solve the following system graphically:

y = 2x + 4

y = 3x + 2

(2, 8)

300

Solve the following system graphically:

x = 3

y = 2x + 1

(3, 7)

400

Solve the following system graphically:

4x + 2y = 8

2x + y = 4

All points along 4x+2y =8

500

Solve the following system graphically:

2x+y=5

4x+2y=-6

no solution

Systems of Equations Substitution

100

Using Substitution, what would the resulting equation be? 

y = 2x+3

3x + 2y = 10

3x+2(2x+3)=10

200

Use substitution: What would the resulting equation be?

x = -3y+2

-x + 2y = 3

-(-3y+2)+2y=3

300

Using substitution, what is the resulting equation?

x - 2y = -10

3x - y = 0

3(2y-10)-y=0

or

x-2(3x)=-10

400

Using substitution, find AND SIMPLIFY the resulting equation. 

2x – 3y = –2

 4x + y = 24

2x-3(-4x+24)=-2

2x+12x-72=-2

14x-72=-2

14x=70

x=5

500

Using substitution, simplify the following system:

5x - y = -13

-5x +2y = 24

5x+26=24

Systems of Equations Elimination

100

Using elimination, what is the resulting equation?

x + 3y = 5

2x -3y = -8

3x=-3

200

Using elimination, what is the resulting equation?

-5y + 8x = -18

5y + 2x = 58

10x=40

300

Solve the following system algebraically:

3y - 5x = -26

-2y - 5x = -16

-5y=10

or

5y=16

400

Use elimination to find the resulting equation.

3x−5y=5

9x−5y=10

6x=5

or

-6x=-5

500

Use elimination to determine the resulting equation

4x−9y=2

12x−5y=-38

22y=-32

Systems of Equations Word Problems

100

Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?

2 fancy shirts and 5 plain shirts

200

Lindsay and Dori are grocery shopping and buying large and small boxes of oranges for their students. Small boxes cost $4, and large boxes cost $12. They bought 12 boxes of fruit in total and spent $120. How many small boxes did they buy?

3 small boxes

300

Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of one senior citizen ticket and one child ticket?

senior citizen ticket = $4

child ticket = $7

400

Puppy adoption fees are $250, adult dog fees are $100. If the shelter adopts 50 dogs and collects $8,000 how many adult dogs were adopted? 

30 adult dogs

500

There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?

6 chickens and 7 pigs

Systems of Inequalities

100

What kind of line would you use to graph this inequality? 

3>2x+5

dotted or dashed

200

Which coordinate is a solution to this system of inequalities? 

A

300

Name two points that solve this system of inequalities. 

y>-4x+3

y<1/8x+2

400

Which coordinate does not solve this system of inequalities? (6,8),(0,4),(-2,8),(0,8)

y>-x+4

y≥2/3x+4

(0,4)

500

Solve the system of inequalities graphically:

2x – 3y < 12 

x + 5y < 20 

Is the point (5, 3) in the solution set?

NO! The point (5, 3) is right on the line and it is dotted so it is NOT included!

Plug in values: 1 < 12        20 < 20 

Miscellaneous

100

What is the name of the school mascot?

Tuffy

200

Name ONE of Mrs. Hulett's dogs names, DOUBLE POINTS if you can also name Mrs. Wilson's dog!

Ryder, Ducky, Potato

Roxy

300

Name 3 assistant principals- double points if you can name all 9!

Tyner, Briscoe, Plane, Case, Eisenmann, Travis, Bunao, Olson, Tucker

400

What grade is Mrs. Hulett AND Mrs. Wilson's son in together?

7th

500

SING (YES SING) the Alma Mater

music!