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Systems of Inequalities
Solving by Graphing
Solving by Elimination
Solving by Substitution
Word Problems
100

This method must be used to solve a system of inequalities

Graphing method

100

Where is the solution? SOLVE BY GRAPHING 

y = x + 4
y = 2x + 5

(-1,3) 

100

The solution to the system of equations:

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

 (-8, 2)

100

The solution to the system:

x = 4y
2x + 3y = 22

(8, 2)

100

The sum of two numbers is 104. Their difference is 68. What system of equations can you write to model this?

x + y = 104

x - y = 68

200
Describe how you would shade y < 3x + 4
What is "underneath" or "where (0,0) is"?
200

What is the solution to the system? SOLVE BY GRAPHING 

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

(0, -2)

200

The solution to the system:

4x + y = 5

x - y = 10

(3, -7)

200

The solution to the system

y = x - 2
3x - y = 16

(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 system of equations can you write to model this?

6x + 8y = 700

9x+ 6y = 660

300
Show your solution to the system y < x + 2 and x > 3
shade under y < x + 2 and to the right of x > 3. Both are dotted lines.
300

What is the solution to the system? SOLVE BY GRAPHING

y = -3
x = 5

 (5, -3)

300

The solution to the system:

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

 (.5, 1)

300

The solution to the system

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

(3, 8)

300

The number of each type of ticket sold in the following situation: 

Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.

Write the system of equations to model the situation

5x +7.50y = 3500

x + y = 600

400

Is (3, -4) a solution to 3x - y > 13

No. 13 = 13 (not greater)

400

What is the solution to the system? SOLVE BY GRAPHING

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

(3, -2)

400

The solution to the system

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

Infinitely many solutions

400

The solution to the system

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

(-2, -5)

400

Tickets to a movies cost $3.oo if purchased before the movie. They cost $5.50 if purchased at the movies. For a particular game, 300 tickets were sold and the receipts were $1700.

Write the system of equations to model the situation

3x + 5.50y = 1700

x + y = 300

500

What type of statements do you have if a system has A.) No solution

B.) Infinitely many solutions?

A.) False

B.) True

500

What is the solution to the system? SOLVE BY GRAPHING

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

No solution

500

The solution to the system:

4x + 3y =120
2x - 3y = 24

(24, 8)

500

The solution to the system

t + u = 12
3t + 4u = 15

(-21, 33)

500

Sarah is selling bracelets and earrings to raise money. Bracelets cost $2 and earrings cost $3. She needs to make at least $500 and has at most 50 bracelets and earrings to sell. Write a system of linear inequalities to model the situation 

2x + 3y > 500

x + y < 50