Systems of Equations

Elimination

100

 x + 3 y = 5

2x - 3y = -8

(-1,2)

200

4x - 3y = 16

5x + 3y = 20 

(4,0)

300

-2x - 9y = -25

-4x - 9y= 23 

(-1,3)

400

4x - 9y = 2

12x - 5y = -38 

(-4,-2)

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

Substitution

100

y = 2

3x + 2y = 10 

(2,2)

200

y = x + 1

2x + y =10 

(3,4)

300

y = 5x - 1

2y = 3x + 12

(2,9)

400

2x - 3y = -2

y= -4x + 24

(5,4)

500

x + y = 10

-y = 5 + x

no solution 

Graphing

100

y = 2x + 2

y = x - 1 

(3,-4)

200

y = 2x + 5

y = x + 3

(-2,1)

300

3x - 2y = 8 

x + y = 6

(4,2)

400

y = 1/2x + 2

y = 1/4x + 4

(8,6)

500

4x - 5y = 15

8x + 5y = 45

(5,1)

Vocabulary

100

what are the 3 methods of solving systems of equations  

elimination 

graphing 

substitution 

200

there are two graphs on the same coordinate plane

systems of equations 

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 does it mean when the lines are parallel or they have the same slope and different y-intercepts or when you solve the equations and get a false statement with no variables remaining.

no solution 

500

The method of solving equations where you add or subtract equations to end up with one variable.

elimination