Solving Systems of Inequalities Algebraically

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

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

• x+y≤300
  7.5x+5.5y≥2000

• x+y<300
  7.5x+5.5y≥2000

• x+y≤300
  7.5x+5.5y≤2000

• x+y>2000
  7.5x+5.5y≤300

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

• b + t < 15
  3b + 6t > 66

• b + t > 15
  3b + 6t < 66

• 3b + 6t > 15
  b + t < 66

• 3b + 6t < 15
  b + t < 66

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

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)

Tags

CCSS.HSA.REI.D.12

Select ALL the possible solutions to the system of linear inequalities.

Tags

CCSS.HSA.REI.D.12

Which of the following is a solution to this system of inequalities?

(a)  

• (2,6)

• (0,0)

• (-4,3)

• (6,2)

Tags

CCSS.HSA.REI.D.12

​ ​ (a)   ​ ​ (b)  

Tags

CCSS.HSA.REI.D.12

Which of the following is not a solution to this system of inequalities?

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

Tags

CCSS.HSA.REI.D.12

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

• (0, -2)

• (-3, 0)

• (-3, 2)

• (1, 1)

Tags

CCSS.HSA.REI.D.12