Solutions to Systems
How many solutions can a system of equations have?
1, none, or infinitely many
The graph of a system of equations with no solution looks like __________ ____________.
The graph of a system of equations with no solution looks like __parallel__ __lines____.
Graph to find the solution to the system:
y=2x+1
y=-2x+1
Solution: (0,1)
What is slope-intercept form?
y=mx+b
Without graphing, determine how many solutions the system of equations has.
y=2x+5
y=3x
One!
The graph of a system with infinitely many solutions looks like the ___________ ___________.
The graph of a system with infinitely many solutions looks like the ____same_____ ____line___.
Graph to find the solution to the system:
y=5
x=-2
Solution: (-2,5)
What is the slope-intercept form of this equation:
y-2=4x
y=4x+2
When looking at the equations for a given system if the system has infinitely many solutions you will find the m values are the ____________ and the b values are the ______________.
When looking at the equations for a given system if the system has infinitely many solutions you will find the m values are the ____same____ and the b values are the ___same____.
The graph of a system with one solution looks like ____________ ______________.
The graph of a system with one solution looks like ___intersecting__ ___lines__.
Graph to find the solution to the system:
y=(3/2)x - 1
y= (1/2)x +3
Solution: (4,5)
What is the slope intercept form of this equation?
x+y=45
y=-x+45
When looking at the equations for a given system if the system has one solution you will find the m values are __________ and the b values _________.
When looking at the equations for a given system if the system has one solution you will find the m values are __different___ and the b values __don't matter___.
How many solutions are there to a system of equations with 2 vertical lines?
none!
Graph to find the solution to the system:
y = x + 2
y = -2x - 1
Solution: (-1,1)
What is the slope-intercept form of this equation?
2y = 6x-4
y=3x-2
Without graphing, determine how many solutions the system of equations has.
y=2x+1
2x=y+7
None!
When given a graph with 2 or more lines, how can you tell how many solutions to the system of equations there will be?
A solution to a system of equations is a point on both (or all) lines.
If they cross at one point, they have one solution.
If they never cross there is not solution.
If they are the same line there are infinitely many solutions.
Graph to find the solution to the system:
3x + y = 1
y = 4x + 1
Solution: (0,1)
What is the slope-intercept form of this equation?
6=9x+3y
y=-3x+2