Systems of Equations and Inequalities

Your family goes to a southern style restaurant for dinner. There are 6 total people in your family. Some order chicken for $14 and the rest order steak for $17. The total bill is $99. Write a system that could represent this situation.

• c + s = 6
  14c + 17s = 99

• c + s = 99
  14c + 17s = 6

• c + s = 6
  17c + 14s = 99

• c + s = 99
  17c + 14s = 6

Solve using substitution.
x - 2y = 2
3x + 4y = 3

• (1.4, -0.3)

• (3.1, 5)

• (-2.5, 3.5)

• (6.9, 1.02)

Solve using substitution.
2x - 2y = 2
y = -5x + 14

• (4, 5)

• (2.5, 1.5)

• (1.5, 5)

• (1, 2.25)

Are the points on the boundary line part of the solution set or not?

• Yes, they are part of the solution set

• No, they are NOT part of the solution set

Match: the overlap is on the left!

• y ≤ 3x   and  y ≤ -2x + 4

• y > 3x   and  y > -2x + 4

• y < 3x   and  y > -2x + 4

• y > 3x   and  y < -2x + 4

Select the correct graph for each inequality.

• A

• B

• C

• D

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

Which system of inequality is shown?

• y ≥ -x - 1
  y < x + 4

• y < -x - 1
   y ≥ x + 4

• y > -x - 1
  y ≥ x + 4

• y = -x - 1
  y ≥ x + 4

You can work at most 20 hours next week. You need to earn at least $92 to cover you weekly expenses. Your math tutoring job pays $7.50 per hour and your job as a pet sitter pays $6 per hour. You can work at most 7 hours tutoring. Write a system of linear inequalities to model the situation.

• s + t < 20
  6s + 7.50t ≥ 92
  t >7

• s + t ≤ 20
  6s + 7.50t ≥ 92
  t ≤ 7

What is the solution?

• (6, 3)

• (3, 6)

• (-6, 3)

• No solution