Elimination
Substitution
Graphing
Vocabulary
100
x + 3 y = 5
2x - 3y = -8
(-1,2)
100
y = 2
3x + 2y = 10
(2,2)
100
y = 2x + 2
y = x - 1
(3,-4)
100
what are the 3 methods of solving systems of equations
elimination
graphing
substitution
200
4x - 3y = 16
5x + 3y = 20
(4,0)
200
y = x + 1
2x + y =10
(3,4)
200
y = 2x + 5
y = x + 3
(-2,1)
200
there are two graphs on the same coordinate plane
systems of equations
300
-2x - 9y = -25
-4x - 9y= 23
(-1,3)
300
y = 5x - 1
2y = 3x + 12
(2,9)
300
3x - 2y = 8
x + y = 6
(4,2)
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
4x - 9y = 2
12x - 5y = -38
(-4,-2)
400
2x - 3y = -2
y= -4x + 24
(5,4)
400
y = 1/2x + 2
y = 1/4x + 4
(8,6)
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 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
500
x + y = 10
-y = 5 + x
no solution
500
4x - 5y = 15
8x + 5y = 45
(5,1)
500
The method of solving equations where you add or subtract equations to end up with one variable.
elimination