Can you look at a system of linear
equations and tell how many
solutions it has?
For example:
Could you tell that the equations
y=2x +1 and y= 2x-7 have no
solution?
In this lesson you will learn
to predict how many
solutions a system of linear
equations has by inspection.
Let’s
Review
Let’s
Review
Slope Intercept Form of an Equation
y = mx + b
slope
y-intercept
Let’s
Review
Let’s
Review
Graphing a linear equation
y = 2x + 1
slope
y-intercept
Let’s
Review
Let’s
Review
y = 2x + 1
A Common
Let’s
Review Mistake
Assuming that all equations have one
solution because those are the types of
equations that are solved the most.
CoreReview
Lesson
Let’s
There are three types of solutions
for systems of linear equations
One
None
Infinitely Many
CoreReview
Lesson
Let’s
y = 2x + 1
y = 3x + 1
One point
one solution
1
y= x-5
2
1
y= x-3
2
Parallel lines
no solution
y = 4x +4
y = 4(x+1)
Same Line
infinitely many
solutions
CoreReview
Lesson
Let’s
Determine the number of solutions
that the system has.
y = -4(x+4)
Slope: -4, y-intercept: -16
y = -4x-16
y = -4x-16
Slope: -4, y-intercept: -16
CoreReview
Lesson
Let’s
Determine the number of solutions
that the system has.
y=x+1
Slope: 1, y-intercept: 1
1
y= x+1
2
1
Slope: , y-intercept: 1
2
CoreReview
Lesson
Let’s
Determine the number of solutions
that the system has.
y = -5x + 1
Slope: -5, y-intercept: 1
y = -5x-2
Slope: -5, y-intercept: -2
In this lesson you learned to
predict how many solutions a
system of linear equations
has by inspection.
Guided
Practice
Let’s
Review
How many solutions does the system of
linear equations have?
y= -2x+1
y= -2x-2
Guided
Practice
Let’s
Review
How many solutions does the system of
linear equations have?
y= -3x+1
y= -2x-7
Guided
Practice
Let’s
Review
How many solutions does the system of
linear equations have?
y= -3(x+1)
y= -3x-3
Extension
Let’s
ReviewActivities
What are the possible number of solutions
for a system of linear equations?
Extension
Let’s
ReviewActivities
Does the system of linear equations y=2x
and y=2x+1 have infinitely many solutions?
Explain your answer.
Extension
Let’s
ReviewActivities
Create a second equation for the
following system of equations so that they
have one solution, no solution, and
infinitely many solutions.
One solution
y = 7x + 1 y=
y = 7x + 1
y=
y = 7x + 1
y=
No solution
Infinitely many
solutions
Quick Quiz
Let’s
Review
How many solutions does the system of
equations have? y=6(x+1) and y=6x+6
a) One b) None c) Infinitely Many
How many solutions does the system
of equations have? y=-3x and y=x+1
a) One b) None c) Infinitely Many