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Systems of inequalities
Systems of equations
Solving by Elimination
Solving by Substitution
Word Problems
100

Graph and screen share 

y > 1 

x + y < 3 

Check graph 

100
The quadrant in which the solution to the following system lies:

y = x + 4
y = 2x + 5

What is II
100
The solution to the system of equations:

r + s = -6
r - s = -10

What is (-8, 2)?
100
The solution to the system:

x = 4y
2x + 3y = 22

What is (8, 2)
100

The sum of two numbers is 104. Their difference is 68. What are the numbers?

What are 86 and 18?

200

What is a feasible region?

The area where both inequalities have viable solutions (double shaded area)

200
The solution to the system of equations:

y = 3x - 2
y = -x - 2

What is (0, -2)?
200
The solution to the system:

8a + 5b = 9
2a - 5b = -4

What is (0.5, 1)?
200
The solution to the system

y = x - 2
3x - y = 16

What is (7, 5)
200

A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. What was the cost of one shirt? Define your variables and set up a systems of equations. 

x = cost of shirt 

y = cost of hat

6x + 8y = 700

9x + 6y = 660

300

Graph the system and give a possible solution 

y >= 2x + 2 

y + 1 > - (x + 4) 

Check graph & point

300
The solution to the system of equations:

y = -3
x = 5

What is (5, -3)
300
The solution to the system:

2x + 3y = 6
3x + 5y = 15

What is (-15, 12)?
300
The solution to the system

y = 3x - 1
7x + 2y = 37

What is (3, 8)
300

Sandra wants to compare phone companies to decide which is better. Call-A-Lot charges $42 per month and $0.50 per minute. ChattyCat charges $2 per minute. Define your variables and set up a system of equations. Determine when both companies will cost the same. 

x = # of months 

y = total cost 

y = 0.50x + 42

y = 2x 

(28, 56) -- At 28 minutes, they will both cost $56. 

400

Can (3, 4) be a possible solution to the system 

y >= -x + 5 

x + y > 8 

No because the solution does not create a true statement for inequality #2. 

400
The solution to the system of equations

y = (1/3)x - 3
2x - y = 8

What is (3, -2)
400
The solution to the system

2a - 4b = 12
-8a + 16b = -48

What is infinitely many solutions?
400
The solution to the system

3s - 2t = 4
t = 2s - 1

What is (-2, -5)
400

Create a word problem where the system would be: 


y = 2x + 10 

y = 3x + 4

Check scenario

500

Sally is buying pens and pencils for her classmates. She needs to buy atleast 26 writing utensils. Pens cost $2 and pencils cost $1, and she can't spend more than $30. Define your variables, write a systems of inequalities, and write the inequalities to include the feasible domain. 

x = # of pens 

y = # of pencils 

x + y >= 26

2x + y <= 30 

x >= 0 and y >=0

500

The solution to the system of equations:

y - 3x = 3
y = 3x - 2

No solution. The lines are parallel.

500
The solution to the system:

(1/3)x + (1/4)y = 10
(1/3)x - (1/2)y = 4

What is (24, 8)
500
The solution to the system

t + u = 12
t = (1/3)u

What is (3, 9)?
500

Each child received money when Mr. Vogel left. He  $25,000 divided between his son and daughter, with the daughter receiving $5000 less than the son.Define your variables, set up your system, solve, and interpret your solution. 

x = $ son received 

y = $ daughter received 

x + y = 25,000 

y = x - 5000

$15,000 for the son and $10,000 for the daughter