2016­2­23 how many solutions.notebook
February 23, 2016
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2/23
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Warm up
Graph the following system and find the intersecting point.
{
y = 2x + 5
1
y = x -1
2
At what ordered pair do these lines intersect?
2016­2­23 how many solutions.notebook
HW Anwers
February 23, 2016
2016­2­23 how many solutions.notebook
February 23, 2016
Lesson 2: Identifying how many solutions a
system has
Student Outcomes:
-Students will identify if a system of
equations has no solution, one solution, or
infinitely many solutions.
Graph the following equations on the same
graph. Label the equations.
m = y = 2x - 3
b = y = 2x + 1
m = b = At what ordered pair do these lines intersect?
2016­2­23 how many solutions.notebook
February 23, 2016
What do we notice about these two lines?
They are parallel
What is the same about the two equations?
y = 2x - 3
y = 2x + 1
Parallel lines have the same slope and different y-intercepts.
They have NO SOLUTIONS
Graph the following equations on the same
graph. Label the equations.
y = -2x + 4
m = b = 2x + y = 4
m = b = At what ordered pair do these lines intersect?
2016­2­23 how many solutions.notebook
February 23, 2016
What do we notice about these two lines?
They overlap
What is the same about these two equations?
y = -2x + 4
2x + y = 4
When the equations in a system have the same slope and the same
y-intercept, they have INFINITELY MANY SOLUTIONS
Graph the following equations on the same
graph. Label the equations.
y=x
m = b = m = y = 2x + 1
b = At what ordered pair do these lines intersect?
2016­2­23 how many solutions.notebook
February 23, 2016
What do we notice about these two lines?
They cross at one point
What is the same about these two equations?
y = 2x + 1
y=x
When the equations in a system have different slopes, they
have ONE SOLUTION
Challenge
Without graphing, can you tell how many
solutions the following systems will have?
y = 5x - 9
y = 8x -2
y = 6x + 2
{ y = 5x + 9 { y - 8x = -2 { y = 3x + 1
2016­2­23 how many solutions.notebook
February 23, 2016
When does a system have NO SOLUTION?
When does a system have INFINITELY MANY SOLUTIONS?
When does a system have ONE SOLUTION?