Systems Of Linear Inequalities

Multiple Choice

How can I tell if an inequality will have a solid line?

• It has an equal sign.
• The symbol is greater than.
• The symbol has "or equal to."
• You just guess.

Multiple Choice

Will my line be solid?
5 ≥ x

• Yes
• No

Multiple Choice

Which point is a solution?

• (0, 6)
• (-3, 4)
• (1, 0)
• (-4, 3)

​Graphing Inequalities Reminder

Multiple Choice

For the inequality, $$y\ge-\frac{1}{4}x-3$$   is the line solid or dashed?

• Solid because the inequality includes "equal to"

• Solid because it is "greater than"

• Dashed because the slope is negative

• Dashed because y-intercept is negative

Multiple Choice

For the inequality, $$y<-3x+4$$  is the graph shaded above or below the line?

• Below the line because the inequality includes "less than"

• Below because it is a negative slope

• Above because the y-intercept is positive

• Above because the inequality does not include "equal to"

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 Select

What are the inequalities for this system of inequalities?

• $$y<x-2$$  

• $$y\ge-3x+2$$  

• $$y\ge-1x-2$$  

• $$y\ge-\frac{1}{3}x+2$$  

Multiple Select

What are the inequalities for this system of inequalities?

• $$y<-\frac{1}{2}x+3$$  

• $$y<3x-4$$  

• $$y<-2x+3$$  

• $$y<\frac{1}{3}x-4$$  

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.

Multiple Choice

Is (0,0) a solution to this system of inequalities?

$$y>-x+2$$  

$$y<-5x+2$$  

• yes

• no

• no solution

Multiple Choice

Is (1,1) a solution to this system of inequalities?

$$5x+1>y$$  

$$3x-6y\le6$$  

• yes

• no

• no solution

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

• 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

Multiple Choice

Use desmos to pick the correct graph of the system:
$$y<x$$  
$$y\ge-\frac{1}{2}x+1$$  

Multiple Choice

The graph shows which system?

• 
  

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

  
  $$y\le-5x+10$$
  

• $$y<\frac{2}{3}x+1$$
  $$y\ge-5x+10$$
  

• $$y<\frac{2}{3}x+1$$
  $$y\le-5x+10$$
  

• $$y>\frac{2}{3}x+1$$
  $$y\ge-5x+10$$
  

Multiple Choice

Which point is a solution to both inequalities?

• (-10,-5)

• (-20,25)

• (40,30)

• (40,-10)

Multiple Select

Pick ALL correct answers.

Which are solutions to the system?

• (-5,4)

• (-5,-2)

• (0,10)

• (5,10)

• (0,-5)

Poll

How comfortable are you with system of inequalities?

• I know what I am doing

• I am not fast but I understand

• I am a getting there.

• I am entirely lost