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 ReviewLet’s Review

Slope Intercept Form of an Equation

y = mx + b

slope y-intercept

Let’s ReviewLet’s Review

Graphing a linear equation

y = 2x + 1

slope y-intercept

Let’s ReviewLet’s Review

y = 2x + 1

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

Let’s ReviewQuick Quiz

How many solutions does the system of equations have? y=6(x+1) and y=6x+6a) 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