Solutions
The two lines meet at one point
Find the solution to the following:
y=4x+2 and y=2x
(-1, -2)
Is there one solution, none, or infinite to the following without graphing?
y=3x + 1 and y=3x
None - parallel
When two equations have the same slope and different y-intercepts, what must be true?
They are parallel - no solution - never meet
When two equations are exactly the same there are infinite solutions.
True
There are infinite solutions when...
The two lines are the same (overlap everywhere)
Find the solution to the following:
y=x and y=-x
(0,0)
Is there one solution, none, or infinite to the following without graphing?
y=5x + 15 and y=5x + 15
Infinite
When two equations are exactly the same, what must be true?
They are the same line - infinite solutions
When two equations meet at one point there are exactly two solutions.
False
There is no solution when...
The two lines are parallel (same slope) - never touch
Find the solution to the following:
y=10x - 5 and y=5(2x - 1)
Infinite Solutions
Is there one solution, none, or infinite to the following without graphing?
y=2x + 8 and y=1x + 8
One solution
When the slopes are different for two equations, what must be true?
There is one solution - they must meet
When two lines are parallel to each other that means they have no solutions.
Give an example of two equations with infinite solutions.
Answers Vary - Ex: y=6x+2 and y=2(3x+1)
Find the solution to the following:
y=4x + 4 and y=4x - 10
No solution - parallel
Is there one solution, none, or infinite to the following without graphing?
y=8x+10 and y=-8x+10
One Solution
If you are unsure what the solution is, what options do you have?
Graph or Plug in for a variable and solve
Two lines can meet at exactly two points and therefore have only two solutions.
False - they either meet at one, none, or all
Give an example of two equations with no solution.
Answers Vary - Ex: y=2x + 1 and y=2x - 1
You graphed your two equations but only see one line, what is your solution?
Infinite because it's the same line.
Is there one solution, none, or infinite to the following without graphing?
y=5x+15 and y=5(1x+3)
Infinite Solutions
You know the slopes are the same, what two options do you have for your solutions?
No solution - if different y-intercepts
Infinite solutions - if everything is the same
When the slopes are the same, there has to be exactly one solution.
False