Unit 6 Review - Linear Systems

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.   On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25
  5c + 10d = 16.50
• 10c + 5d = 16.50
  5c + 10d = 14.25
• c + d = 10
  5c + 10d = 16.50
• c + d = 5
  5c + 10d = 16.50

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system of equations to represent this situation.

• a + c = 21

  6a + 4c = 104

• a + c = 21

  4a + 6c = 104

• a + c = 104

  6a + 4c = 21

• a + c = 104

  4a + 6c = 21

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Write a linear system to model this situation.

• 7a + 6c = 150

  11a + 6c = 227

• 7a + 6c = 227

  11a + 6c = 150

• 6a + 6c = 150

  7a + 11c = 227

• 6a + 6c = 227

  7a + 11c = 150

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount? 

• y = 6.80 + .65x
  y=7.30+.90x
• x + y = 6.80
  x + y = 7.30
• y = 6.80+.90x
  y = 7.30 + .65x
• y + .90x = 6.80
  y + .65x = 7.30

Which of the following is a solution to the systems of inequalities?

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)

Which of the following is a solution to the systems of inequalities?

• (0, -2)

• (-3, 0)

• (-3, 2)

• (1, 1)

Which of the following is a solution to the systems of inequalities?

• (0, 0)

• (1, 1)

• (-4, -2)

• (4, -2)

Which system of linear inequalities is represented by the graph?

• y≤2x-1
  y>-2x+3
• y>2x-1
  y≤-2x+3
• y<2x-1
  y≥-2x+3
• y≤2x-1
  y>2x+3

Solve the system of inequalities by graphing.

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Colin needs to save at least $200 for homecoming. He works 2 jobs earning $9/hour at Wawa and $25/hour mowing lawns. He only has time to work 16 hours before homecoming.

• x + y ≥ 25

  x + y ≤ 9

• 100x + 25 y ≤ 200

  2x + 9y ≤ 16

• x + y ≥ 200

  9x + 25y ≤ 16

• 9x + 25y ≥ 200

  x + y ≤ 16