Systems of Nonlinear Inequalities

Is (-2,4) a solution to the system?

• Solution

• Not a solution

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

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans she plants and $3,000 for every acre she plants with barley can be modeled by P=4000x+3000y . If x represents acres of soybeans and y represents acres of corns, which inequalities represent the possible solutions to her situation?

• x≥0

  y≥0

  x+y≥6

  3x+2y≥15

• x≥0

  y≥0

  x+y≤6

  2x+3y≤15

• x≥0

  y≥0

  4000x+y≤6

  2x+600y≤15

• P=4000x+3000y

Identify the solutions to the system of inequalities. Select all that apply.

• (0, 0)

• (4, 0)

• (0, 4)

• (-2, 0)

Identify the solutions to the system of quadratic inequalities. Select all that apply.

• {(0, 1)}

• {(1, 0)}

• {(-1, 0)}

• {(0, -1)}

Determine the system of inequalities. Select two inequalities.

Determine the system of inequalities. Select two inequalities.

Lisa gives child(x) and adult(y) haircuts in her salon. She charges $10 for a child and $40 for an adult haircut. Her goal is to make at least $1000 per week and work no more than 40 hours. The shaded region of the graph represents the possible combinations of adult and child haircuts that will allow her to meet her goal. Which combination represents her maximum profit?

• 10 adult haircuts and 60 child haircuts

• 20 adult haircuts and 40 child haircuts

• no adult haircuts and 80 child haircuts

• 40 adult haircuts and no child haircuts

Determine the system of inequalities. Select two inequalities.