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?
Dec 18, 2015
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 ReviewA Common Mistake
Assuming that all equations have one solution because those are the types of equations that are solved the most.
Let’s ReviewCore Lesson
There are three types of solutions for systems of linear equations
One None Infinitely Many
Let’s ReviewCore Lesson
y = 2x + 1
y = 3x + 1
One pointone solution
y = 4x +4
Same Line
infinitely many solutions
Parallel lines no solution
y = x - 5
y = x - 3 y = 4(x+1)
Let’s ReviewCore Lesson
Determine the number of solutions that the system has.
y = -4(x+4)
y = -4x-16
Slope: -4, y-intercept: -16
Slope: -4, y-intercept: -16
y = -4x-16
Let’s ReviewCore Lesson
Determine the number of solutions that the system has.
y = x + 1
y = x + 1
Slope: 1, y-intercept: 1
Slope: , y-intercept: 1
Let’s ReviewCore Lesson
Determine the number of solutions that the system has.
y = -5x + 1
y = -5x-2
Slope: -5, y-intercept: 1
Slope: -5, y-intercept: -2
In this lesson you learned to predict how many solutions a
system of linear equations has by inspection.
Let’s ReviewGuided Practice
How many solutions does the system of linear equations have?
y= -2x+1
y= -2x-2
Let’s ReviewGuided Practice
How many solutions does the system of linear equations have?
y= -3x+1
y= -2x-7
Let’s ReviewGuided Practice
How many solutions does the system of linear equations have?
y= -3(x+1)y= -3x-3
Let’s ReviewExtension Activities
What are the possible number of solutions for a system of linear equations?
Let’s ReviewExtension Activities
Does the system of linear equations y=2x and y=2x+1 have infinitely many solutions? Explain your answer.
Let’s ReviewExtension Activities
Create a second equation for the following system of equations so that they have one solution, no solution, and infinitely many solutions.
y = 7x + 1 y=
y = 7x + 1 y=
y = 7x + 1 y=
One solution
No solution
Infinitely many solutions