Graphing
Substitution
Elimination
Linear Inequalities
Vocab
Don't say 10!
100

y = 2x + 2

y = x - 1

(-3, -4)

100

y = 2

3x + 2y = 10

(2, 2)

100

x + 3y = 5

2x -3y = -8

(-1, 2)

100
What does a dotted line mean when graphing linear inequalities?
> or <
100
Consists of two or more linear equations in the same variables.
System of linear equations (linear system)
100

This is the sum of 7 and 3

(5 x 2)

200

y = 2x + 4

y = 3x + 2

(2, 8)

200

x + 3y = 2

-x + 2y = 3

(-1, 1)

200

-5y + 8x = -18

5y + 2x = 58

(4, 10)

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
200

What is the solution to the system x = 10, y=10?

(x, x)

300

x = 3

y = 2x + 1

(3, 7)

300

x - 2y = -10

3x - y = 0

(2, 6)

300

3y - 5x = -26

-2y - 5x = -16

(4, -2)

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.
300

This is the product of 55 and 2

100+5+5

400

4x + 2y = 8

2x + y = 4

No solution

400

2x – 3y = –2

 4x + y = 24

(5, 4)

400

3x−4y=8

18x−5y=10

(0, -2)

400

y≤x−2

y>−3x+5

Shaded toward the bottom right

400
A linear system with no solution, when the graphs of the equations are parallel
Inconsistent system
400

Wimbeldon and The French Open are championships associated wtih this sport

(5+5)nis

500

y = 1/2 x + 2

y = 1/4 x + 4

(8, 6)

500

5x - y = -13

-5x +2y = 24

no solution

500

4x−9y−2=0

12x−5y+38=0

(-4, -2)

500

2x – 3y < 12 

x + 5y < 20 

Darkly shaded top left corner

500
A linear system with infinitely many solutions, when the graphs of the equations are the same
Consistent dependent system
500

This is the solution to the system  x + y = 9 and x - y = 9

What is (0, 9)