What happens if we graph a system of equations and the lines are the

same?

y = 2(2x+4)y = 4x+8

In this lesson you will determine if a system of two

linear equations in two variables has infinitely many

solutions by graphing.

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 MistakeThinking that all systems of equations

must have one solution

Let’s ReviewCore Lesson

Graph the system of linear equations. Determine their solution.

y = 2(2x+4) y – 4x = 8y = 4x+8 +4x =

+4xy = 4x + 8

Let’s ReviewCore Lesson

Graph the system of linear equations. Determine their solution.

y = 2(2x+4)

y = 4x+8

Slope: 4, y-intercept: 8

Slope: 4, y-intercept: 8

y = 4x+8

Let’s ReviewCore Lesson

y = 2(2x+4)

y = 4x+8

y = 4x+8

Let’s ReviewCore Lesson

Graph the system of linear equations. Determine their solution.

x -y = -1 y =x-2+3y =x+1 -x =-x

-y = -1-x -1 = -1 y= 1 +x y= x + 1

Let’s ReviewCore Lesson

Graph the system of linear equations. Determine their solution.

y =x+1

y =x-2+3

Slope:1, y-intercept: 1

Slope:1, y-intercept: 1y =x+1

Let’s ReviewCore Lesson

y =x-2+3

y =x+1

y =x+1

In this lesson you learned to determine if a system of two

linear equations in two variables has infinitely many

solutions by graphing.

Let’s ReviewGuided PracticeFind the solution for the system of linear equations y-3x = 3 and y = 3(x+1) by graphing.

Let’s ReviewGuided Practice

y-3x = 3 y =3(x+1)

Let’s ReviewGuided Practice

y =3(x+1)

y-3x = 3

Let’s ReviewGuided PracticeFind the solution for the system of linear equations y=2x-2+4 and y=2(x+1) by graphing.

Let’s ReviewGuided Practicey=2x-2+4 y= 2(x+1)

Let’s ReviewGuided Practicey=2x-2+4

y= 2(x+1)

Let’s ReviewExtension Activities

When we solve the systems of equations y=2x+2 and y=2(x+1), what is our solution? What does it mean?

Let’s ReviewExtension Activities

How many solutions does the system of equations y=-3x-3 and y=-3(x+1) have? Why?

Let’s ReviewExtension Activities

Create a system of linear equations that have infinitely many solutions.

Let’s ReviewQuick Quiz

The solution for the system of linear equations y=2x+1 and y=2x-3 is?a) One solution b)Infinitely Many Solutions

The solution for the system of linear equations y=4x-12and y=4(x+3)is?a) One solution b) Infinitely Many Solutions