Systems of Equations and Inequalities

Systems of Equations 1

100

 x + 3y = 7

8x - 3y = 2

(1,2)

200

4x - 3y = 16

5x + 3y = 20 

(4,0)

300

-2x - 9y = -25

-4x - 9y= -23 

(-1,3)

400

What is the name for a group of porcupines? 

A. A Pack

B. A Colony

C. A Prickle

D. A Troop

C. A Prickle 

500

The equations 5x + 2y = 48 and 3x + 2y = 32 represent the money collected from school concert tickets sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket?

x=$8

Systems of Equations 2

100

What is the solution to the system?

y = 2x + 2

y = x - 1 

(3,-4)

200

What is the solution to the system?

y = 2x + 5

y = x + 3

(-2,1)

300

What is the solution to the system?

3x - 2y = 8 

x + y = 6

(4,2)

400

What is the solution to the system?

y = 1/2x + 2

y = 1/4x + 4

(8,6)

500

What is the solution to the system?

4x - 5y = 15

8x + 5y = 45

(5,1)

Vocabulary

100

                     **Daily Double**

What is the least common blood type among Americans?

• O +
• O -
• A +
• A -
• B +
• B -
• AB +
•  AB -

AB -

200

What type of solution do parallel lines have?

No Solution

300

How can you tell if a linear system has infinitely many solutions?

 the equations are the same and the lines lie on top of each other 

400

What are the three types of solutions to a system of equations?

one solution

no solution

infinite solutions

500

What happens to the inequality symbol when you divide both sides by a negative number?

Flip the inequality symbol

Systems of Inequalities 1

100

Graph the system of inequalities.

y >2

y < 2x - 4

Is (0,0) a solution to the system? Why?

No

200

 y<=1/2x+5 

 y>1/2x-5 

Is (-10,0) in the solution set of the above system? Why?

No, because (10,0) is on the dotted line of the second inequality.

300

Graph the system of inequalities.

y < 5x - 1

y > 3x + 12

Is (-10,-40) in the solution set? Why?

No, because (-10,-40) is not in the overlapping shaded region.

400

Graph the system of inequalities.

2x-3y<=-2

y>=-4x+24

is (5,4) a solution to the system? Why?

Yes, (5,4) is a solution to the system because the point is on the solid line of both inequalities.

500

 

250x+50y<=4500

Systems of Inequalities 2

100

when graphing linear inequalities what does < and > mean (type of line).

Use a Dotted Line

200

what does  ≤ and ≥ mean when graphing linear inequalities (type of line)

solid line

300

In the graph of y ≤ x, which quadrant is completely shaded?  

Quadrant IV

400

How is graphing systems of inequalities different than graphing systems of equations?

they use dotted lines sometimes and you have to shade to find the solution 

500

Graph of the system using Desmos.

y ≤ x − 2

y > −3x + 5

Is (5,2) a solution to the system?