Graphing Systems of Inequalities

Presentation

•

Mathematics

•

9th Grade

•

Medium

•

CCSS

HSA.REI.D.12, 8.EE.C.8B, 8.EE.C.8A

Standards-aligned

Victor Castillo

Used 4+ times

FREE Resource

18 Slides • 36 Questions

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)

Graphing Linear Inequalities

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

How would you graph the following linear inequality?

y ≥ 4

Dashed line, shade above

Dashed line, shade below

Solid line, shade above

Solid line, shade below

Multiple Choice

How would you graph the following linear inequality?

$y\ ≤\ \frac{4}{3}x\ -\ 4$

Dashed line, shade above

Dashed line, shade below

Solid line, shade above

Solid line, shade below

Multiple Choice

y < 2x - 5

y > 2x - 5

y ≤ 2x - 5

y ≥ 2x - 5

Multiple Choice

Graphing Linear Inequalities:

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

(0, 0)

(0, 1)

(-100, -3)

(5, 10)

Multiple Choice

y < -4

y > -4

y ≤ -4

y ≥ -4

Multiple Choice

y < 3/5x - 5

y > 3/5x - 5

y ≤ 3/5x - 5

y ≥ 3/5x - 5

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

Steps to Graphing Systems of Inequalities

Make sure both inequalities are in Slope-Intercept Form.
Graph both inequalities (Don't forget to determine dashed or solid line and shade above or shade below).
Heavily shade in the portion where the shaded regions overlap. This is the solution to the system of inequalities.

Multiple Choice

What is the equation of the graph?

$y>2x+1$

$y>\frac{1}{2}x+1$

$y<2x+1$

$y<\frac{1}{2}x+1$

Multiple Choice

What is the equation of the graph?

$y<2x-4$

$y<\frac{1}{2}x-4$

$y>2x-4$

$y>\frac{1}{2}x-4$

Systems of Inequalities

Graphing systems of inequalities is simply placing two inequalities on the same graph.
The solution is where the shaded areas overlap
If you can graph one inequality, you can graph two of them on the same graph!

Multiple Choice

A solution to system of inequalities will...

satisfy both inequalities

satisfy at least one inequality

not satisfy either inequality.

Satisfy means make it a true statement.

4>3 is a true statement.

We will start by graphing.

Multiple Select

To graph:

$y<3x-2$

Select all that apply.

y-intercept = -2

slope = 3

solid line

dotted line

shade above

shade below

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

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?

Type response here

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.}

Type response here

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)

System of Inequalities

Is made up of 2 or more linear inequalities.

Solution to a System of Inequalities

Is all ordered pairs that make ALL inequalites true.

**WHERE THE SHADED PORTIONS OF THE BOTH INEQUALITIES OVERLAP.**

Multiple Choice

Given the graph, determine which is NOT a solution.

(0, 0)

(2, -1)

(-2, -2)

(-5, 1)

Multiple Choice

Is (-2, 0) a solution to the system?

Solution

Not a solution

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Given the system, determine a solution.

No solution

Infinite solutions

(-5, 5)

(5, -5)

Multiple Choice

Solve the system of inequalities by graphing. $8x\ +4y\ge10\ and\ 3x-6y>12$

Multiple Choice

Identify the graph represented by the following system of inequalities.

2x - y > 4

4x + 2y < 6

Multiple Choice

How many solutions will this system have?

No solution

One Solution

I Don't Know

Infinitely Many Solutions

Multiple Choice

If a system of linear equations has one solution, what does this mean about the two lines?

Parallel lines

the same line

Intersecting lines

Multiple Choice

What is the solution to this system?

One Solution

No solution

Infinitely Many Solutions

Multiple Choice

Based on the equations for each line, determine how many solutions the system would have.

y=2x+3

y=-4x+3

Infinite Number of Solutions

No Solution

One Solution

Multiple Choice

Based on the equations for each line, determine how many solutions the system would have.

y=5x+3

y=5x-2

Infinite Number of Solutions

No Solution

One Solution

Multiple Choice

Based on the equations for each line, determine how many solutions the system would have.

y=-3x+2

Infinite Number of Solutions

No Solution

One Solution

Match

Match the following graphs to the systems of equations

$y=\frac{2}{3}x+1$

$y=\frac{2}{3}x-2$

$y=-x+7$ $y=2x+1$

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

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

Show answer

Auto Play

Slide 1 / 54

SLIDE

Similar Resources on Wayground

48 questions

Periodic Table of Elements

Presentation

•

8th Grade

47 questions

HYDROSPHERE Review TEKS: E.6A E.4C, E.5B, E.9ABC

Presentation

•

9th Grade

47 questions

Ways to Prove Triangles Congruent

Presentation

•

9th - 10th Grade

52 questions

Unit 4 AP Exam Review

Presentation

•

9th Grade

45 questions

Real Numbers and Operations With Integers

Presentation

•

9th - 10th Grade

47 questions

Life in the Earth System

Presentation

•

9th Grade

46 questions

Transcription and Translation

Presentation

•

9th Grade

50 questions

reasoning and proof

Presentation

•

8th Grade

Popular Resources on Wayground

10 questions

Safety Day 2026 – Student Review

Quiz

•

9th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

20 questions

Parts of Speech

Quiz

•

5th Grade

16 questions

Subject & Predicate

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

Map Skills

Quiz

•

3rd Grade

22 questions

Continents and Oceans

Quiz

•

5th Grade

15 questions

Rounding Decimals

Quiz

•

5th Grade

Discover more resources for Mathematics

12 questions

Absolute Value Equations

Quiz

•

9th Grade

20 questions

Function or Not a Function

Quiz

•

8th - 9th Grade

11 questions

Slope from 2 points

Quiz

•

8th - 9th Grade

10 questions

Exploring the Basics of Exponents

Interactive video

•

6th - 10th Grade

10 questions

Solving Absolute Value Equations

Quiz

•

9th Grade

18 questions

SB 12.2 Write in point slope form

Quiz

•

9th Grade

12 questions

Identify Rigid Transformations

Quiz

•

8th - 12th Grade

10 questions

Complementary, Supplementary, Vertical, and Linear Pairs

Quiz

•

9th - 12th Grade