(04/28) ALG 2 Unit 6B: Solving System of Inequalities Day 2

(04/28) ALG 2 Unit 6B: Solving System of Inequalities Day 2

The graph of a system of linear inequalities should show the region of the graph where the points are solutions to all the inequalities in the system.

Here is the system of the graph

•  $y<-2x-1$  

•  $y\ge x-4$  

Multiple Choice

Which point is a solution?

• (0, 6)
• (-3, 4)
• (1, 0)
• (-4, 3)

Multiple Choice

Chase and Sarah went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for $3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?

• 5g + 3g = 3.60

  2f + 10g = 5.70

• 5f + 2g = 3.60

  3f + 10g = 5.70

• 5f + 2g = 5.70

  3f + 10g = 3.60

• 5f + 3g = 5.70

  2f + 10g = 3.60

Multiple Choice

Jonah is going to the store to buy candles. Small candles cost $3.50 and large candles cost $5.00. He needs to buy at least 20 candles, and he cannot spend more than $80. Write a system of linear inequalities that represent the situation.

• 
  

  $x+y\le20$
  

  $3.5x+5y\ge80$
  
  

• $xy\ge20$
  $3.5+5y\le80$
  

• $x-y\ge20$
  $3.5x+5y\le80$
  

• $x+y\ge20$
  $3.5x+5y\le80$
  

Multiple Choice

Marsha is buying plants and soil for her garden. The soil cost $4 per bag, and the plants cost $10 each. She wants to buy at least 5 plants and can spend no more than $100. Write a system of linear inequalities to model the situation.

• 
  

  $4x+10y\ge100$
  

  $x\le5$
  
  

• $4x-10y\le100$
  $x\ge5$
  

• $4x+10y\le100$
  $y\ge5$
  

• $4x-10y\ge100$
  $y\le5$
  

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Which ordered pair(s) is a solution to the given system?

• (5, -5)

• (0,0)

• (-5, -2)

• (3,-3)

How to set up inequalities

Example 1: You can work at most 20 hours next week. You need to earn at least $92 to cover your weekly expenses. Your dog-walking job pays $7.50 per hour and your job as a car wash attendant pays $6 per hour. Write a system of linear inequalities to model the situation.

Breaking up the problem

Example 1: You can work at most (can't go over 20 use less than or equal to symbol) 20 hours next week. You need to earn at least (you can make more than 92 dollars. Use greater than or equal to symbol) $92 to cover your weekly expenses. Your dog-walking job (represented by x) pays $7.50 per hour and your job as a car wash attendant (represented by y) pays $6 per hour. Write a system of linear inequalities to model the situation.

Multiple Choice

Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function for this region.
3 ≤ y ≤ 6
y ≤ 3x + 12
y ≤ -2x + 6
f(x , y) = 4x - 2y

• The maximum value is 0 at (0, 6). The minimum value is - 20 at (-3, 3).
• The maximum value is 0 at (-3, 3). The minimum value is - 20 at (0, 6).
• The maximum value is 0 at (-2, 6). The minimum value is - 20 at (1.5, 3).
• The maximum value is 0 at (1.5, 3). The minimum value is - 20 at (-2, 6).

Multiple Choice

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

• x + y ≤ 8
• x + y ≤ 6
• 2x + 3y ≤ 6
• x + y ≤ 10

Writing the system with what we know

• x = dog walking job ($7.5 an hour)

• y = car wash attendant ($6.00 an hour)

•  $\le20$  used for working up to 20 hours

•  $\ge92$  used for what you need to earn to cover expenses

• Put it all together to get:

•  $x+y\le20$  

•  $7.50x+6.00y\ge92$