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Graphing
Word Problems
Substitution or Elimination
Linear Inequalities
Vocab
100

Solve by graphing:

y = 2x + 2

y = x - 1

(-3, -4)

100

Write out the two equations, DO NOT SOLVE:

Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220.

3s+14L=203

11s+11L=220

100

Solve the system using substitution or elimination.

x + 3y = 5

2x -3y = -8

(-1, 2)

100

When do you use a dotted line when graphing inequalities?

> or <

100
Consists of two or more linear equations in the same variables.
System of linear equations (linear system)
200

Solve by graphing:

y = 2x + 4

y = 3x + 2

(2, 8)

200

Write out the equations, DO NOT SOLVE: 

You are running a concession stand at a basketball game. 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.

1.50x + 0.50y = 78.50 

x + y = 87

200

Solve the system using substitution or elimination.

2x+3y=8

y=x+1

(1,2)

200
How is graphing systems of inequalities different than graphing systems of equations? (2 things)
Sometimes they use dotted lines and you have to shade for inequalities.
200
The method of solving equations where you add or subtract equations to end up with one variable.
Elimination
300

Solve by graphing:

x = 3

y = 2x + 1

(3, 7)

300

Write out the two equations, DO NOT SOLVE: 

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students.

1v+6b=372

4v+12b=780

300

Solve the system using substitution or elimination.

6x + 7y = 20

y = 2x+10

(-5/2, 5)

300
How do you know where to shade when solving systems of inequalities?
Test a point in the equations. If it's true, shade toward the point. If false, shade away. Where the shaded regions overlap is your solution.
300
How can you tell if a linear system has infinitely many solutions?
The equations are the same or solving the system provides a true statement with no variables.
400

Solve by graphing:

4x + 2y = 8

2x + y = 4

No solution

400

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

Child Ticket: $14

Senior Ticket: $8

400

Solve the system using substitution or elimination.

4x+y=10

2x+y=8

(1,6)

400

Graph and shade the following on your bord:

y≤x−2

y>−3x+5

Shaded toward the bottom right

400

If there is no solution to a system of equations, what do the two equations look like on a graph?

They will be parallel lines

500

Solve by graphing:

y = 1/2 x + 2

y = 1/4 x + 4

(8, 6)

500

You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?

Taco: $1.25

Burrito: $2.50

500

Solve the system using substitution or elimination.

3x−4y=8

18x−5y=10

(0, -2)

500

Graph and shade the following on your board:

2x – 3y < 12 

x + 5y < 20 

Darkly shaded top left corner

500

When two graphed lines are identical, how many solutions will the system have?

Infinitely many solutions