Systems of Inequalities (part 1)

Systems of Inequalities

Objective: Solve Systems of Inequalities

Graphing Inequalities REVIEW

Use the y-intercept and slope the same as before

The symbols ≤ or ≥ mean you use a SOLID LINE

The symbols < or > mean you use a DOTTED LINE

The symbols ≤ and < mean you SHADE BELOW

The symbols ≥ and > mean you SHADE ABOVE

Multiple Select

When graphing  $y\ge-\frac{2}{7}x+1$  , you will draw which of the following.

• A dotted line

• A solid line

• Shade above

• Shade below

Example 2

Graph:  $y>-\frac{2}{3}x+2$  

y-intercept:
slope: 

Solid or Dotted line

Shade above or below

Multiple Choice

Which is the graph for the inequality:  $y>-\frac{1}{4}x+1$  ?

CORRECT ANSWER

> means DOTTED LINE

> means SHADE ABOVE

System of Equations

REVIEW

Graph
 $y=-\frac{1}{2}x-3$  and  $y=3x-10$  

The solution is (2,-4)

WHERE THE LINES CROSS

System of Inequalities

A system of inequalities is TWO or more inequalities graphed in the same plane.

The SOLUTION SET is where the shaded areas overlaps.

Example 1

Solve the system

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

Graph and shade both.

The solution set is the overlap.

Example 1 (answer)

Solve the system

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

Graph and shade both.

The solution set is the overlap.
(where the red and blue shading crosses)

VIDEO

Watch this video if you were absent for the lesson or need to review what we went over in class.

Multiple Choice

Which graph represents the solution set of the following system?

 $y\le-3x+5$  and  $y>-\frac{1}{4}x-3$  

ANSWER

Let's walk through the answer.

Which graph represents the solution set of the following system?

 $y\le-3x+5$  and  $y>-\frac{1}{4}x-3$  
  

ANSWER

If you missed the live lesson.

Graph:  $y\le-3x+5$  

Graph:  $y>-\frac{1}{4}x-3$  

See BOTH on the same graph.

Then JUST the overlap of the shadeed areas.

Multiple Choice

Which graph represents the solution set of the following system?

 $y<\frac{2}{3}x-1$  and  $y\ge-\frac{1}{2}x+2$  

ANSWER

Let's walk through the answer.

Which graph represents the solution set of the following system?

 $y<\frac{2}{3}x-1$  and  $y\ge-\frac{1}{2}x+2$  
  

Multiple Select

Choose both inequalities that would create the graph.

• $y>2x-8$

• $y\ge2x-8$

• $y>\frac{1}{2}x-8$

• $y\le\frac{1}{2}x+2$

• $y\le2x+2$

ANSWER

Use graph to create inequality.

 $y>2x-8$ 

 $y\ge2x-8$  

 $y>\frac{1}{2}x-8$ 

  $y\le\frac{1}{2}x+2$  

 $y\le2x+2$  

VIDEO

This video is an explanation of how to complete the previous question if you were absent.