Graphing System of Inequalities

Graphing Systems of Linear Inequalities

Learning Outcomes:

1. Be able to graph a system of linear inequalities

2. Identify solutions to systems of linear inequalities by graphing

But first...

Let's review some previously learned skills that you can apply to this new concept.

Multiple Choice

Graphing Linear Equations: 

Which graph represents the equation $$y=4x-1$$  

Multiple Choice

Systems of Equations:

What is the solution to this system?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

Multiple Choice

Graphing Linear Inequalities:

Consider the function y < 2x+3. Which is true?

• The line would be solid with shading above.

• The line would be dashed with shading above.

• The line would be solid with shading below.

• The line would be dashed with shading below.

Multiple Choice

Graphing Linear Inequalities:

Which point below is NOT a part of the solution set?

• (0, 0)

• (0, 1)

• (-100, -3)

• (5, 10)

What is a System of Linear Inequalities?

• A set of at least two linear inequalities in the same variables

• To solve a system, you need to find the variable values that will make each inequality true at the same time

We will start by graphing.

 $y<3x-2$ 
  $y\ge x+1$  

Multiple Select

To graph:

$$y<3x-2$$

Select all that apply.

• y-intercept = -2
  
  slope = 3

• solid line
  

• dotted line

• shade above

• shade below

 $y<3x-2$  

• y-intercept = (0,-2)

• slope = 3  or  $\frac{3}{1}$  

• dotted line 

• shaded below

• solution is in the red shaded area

Multiple Select

To graph:

$$y\ge x+1$$

Select all that apply.

• y-intercept = 1
  
  slope = 1

• solid line
  

• dotted line

• shade above

• shade below

 $y\ge x+1$  

• y-intercept = (0,1)

• slope = 1  or  $\frac{1}{1}$  

• solid line 

• shaded above

• solution is in the blue shaded area

Let's make them a system!

Graph both inequalities on the same coordinate plane

But wait...where is the solution?!

Poll

Where do you think the solution will be?

• Blue

• Purple

• Red

• White

• All of blue and all of red

Let's think about systems of equations for a moment...

Open Ended

What makes (1,-1) the solution to the system of equations in the video?

Open Ended

Which area (white, red, purple, blue) do you think represents the solution to this system of inequalities? Explain your reasoning.

_{Remember that a solution makes BOTH inequalities true at the same time.}

Multiple Choice

Which of the following is a solution to the systems of inequalities?

• (-1, -3)

• (3, 0)

• (-2, 2)

• (4, 1)

Multiple Choice

Which of the following is a solution to the systems of inequalities?

• (0, 0)

• (1, 1)

• (-4, -2)

• (4, -2)

Multiple Choice

Which of the following is a solution to the systems of inequalities?

• (0, -2)

• (-3, 0)

• (-3, 2)

• (1, 1)

Multiple Choice

Which of the following is NOT a solution to the systems of inequalities?

• (0, 0)

• (3, -2)

• (3, -4)

• (4, -4)

Multiple Choice

Which of the following is a solution to the systems of inequalities?

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)