Systems of Inequalities

Systems of Inequalities

02/10/2021 - 02/11/2021

Multiple Choice

Bell Ringer!!!

Joe bought 2 pairs of jeans and 1 shirt for $120. Sam bought 1 pair of jeans and 3 shirts for $135. How much does 1 shirt cost?

• $45.00

• $40.00

• $33.75

• $30.00

Multiple Choice

For a party, you can spend no more than $12 on peanuts and

cashews. Peanuts are $2.00/lb. and cashews are twice that. Which graph represents the solution set for this situation?

Systems of Linear Inequalities

A system of linear inequalities is simply two inequalities graphed on the same coordinate plane.  The solution is the “region/section” where the shaded regions/sections overlap.

Graphing Systems of Linear Inequalities

~You will graph each linear inequality separate.

~The part where the shadings overlap is where you will find your solutions

~You can graph this by hand or use the calculator

Graphing linear inequalities by hand

Graphing using a calculator

Multiple Choice

Use desmos. Which correctly shows the graph of the sytem:

 $y<-\frac{3}{2}x+1$  
 $x\ge-2$  

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)

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?

Multiple Choice

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40