Applications: Systems of Equations and Inequalities

What's the difference between systems of equations and systems of inequalities?

• Systems of equations have 1 solution, no solution, or infinite solutions while systems of inequalities can have a range of solutions.

• Systems of equations use slope-intercept form only while systems of inequalities use standard form only.

• Systems of equations have a shaded region while systems of inequalities do not.

• There is no difference.

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CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

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?

• x + y ≥ 6
  32x + 20y ≤ 150

• x + y ≥ 632
  x + 20y ≥ 150

• x + y ≤ 6
  32x + 20y ≤ 150

• x + y ≤ 6
  32x + 20y ≥ 150

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

CCSS.HSA.CED.A.1

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

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

CCSS.HSA.CED.A.1

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

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CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 

• x + y = 6
  14.80x + 17y = 91
• x + y = 91
  14.80x + 17y = 6
• x + y = 6
  14.80y + 17x = 91
• x + y = 91
  14.80x+ 17y = 6

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.C.6

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. How many of each type of ticket were sold?

• 10 adults, 11 children
• 12 adults , 9 children
• 11 adults, 10 children
• 9 adults, 12 children

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.C.6

Select the correct graph for each inequality.

• A
• B
• C
• D

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CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.12

• y < x−2 
  y < 3
• y > -x+2
  y > 3
• y < -x+2
  y < 3
• y < -x+2
  y > 3

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

CCSS.HSA.REI.B.3

Which point is part of the solution?

• (4,0)

• (0,4)

• (10,5)

• (5,10)

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CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.12

CCSS.HSA.REI.D.11

Which point is a solution?

• (0, 6)

• (-3, 5)

• (1, 0)

• (-4, 3)

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CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7