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

parallel?

y = x

y = x - 1

In this lesson you will determine if a system of two

linear equations in two variables has no solution 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 Mistake

Thinking that all systems of equations must have one solution

Let’s ReviewCore Lesson

Graph the system of linear equations. Determine their solution.

y = 2x y - 4 = 2x + 4 = + 4

y = 2x + 4

Let’s ReviewCore Lesson

Graph the system of linear equations. Determine their solution.

y = 2x

y = 2x+4

Slope: 2, y-intercept: 0

Slope: 2, y-intercept: 4

Let’s ReviewCore Lesson

y = 2x

y = 2x+4

Let’s ReviewCore Lesson

Graph the system of linear equations. Determine their solution.

-x + 2y = 0 2y –x = - 2 +x = +x

2y = x

2 = 2 y = x

+x = +x

2y = x - 2

2 = 2 y = x - 1

Let’s ReviewCore Lesson

Graph the system of linear equations. Determine their solution.

y = x

y = x - 1

Slope: , y-intercept: 0

Slope: , y-intercept: -1

Let’s ReviewCore Lesson

y = x - 1

y = x

Let’s ReviewCore Lesson

y = x - 1

y = x

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

linear equations in two variables has no solution by

graphing.

Let’s ReviewGuided Practice

Find the solution for the system of linear equations y = x – 1 and y = x – 5 by graphing.

Let’s ReviewGuided Practice

y = x - 1

y = x - 5

Let’s ReviewGuided Practice

Find the solution for the system of linear equations y=3x and y=3x-2 by graphing.

Let’s ReviewGuided Practice

y=3x

y= 3x-2

Let’s ReviewExtension Activities

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

Let’s ReviewExtension Activities

How many solutions does the system of equations y=3x+1 and y=3x-2 have? Why?

Let’s ReviewExtension Activities

Create a system of linear equations that have no solutions.

Let’s ReviewQuick Quiz

The solution for the system of linear equations y=2x+1 and y=2x-3 is?a) (-1,1) b) (1,-1) c)(-1,-1) d) no solution

The solution for the system of linear equations y=-x+6 and y=-x-2 is?a) (2,-4) b) (-2,4) c) (-2,-4) d) no solution