Unit 3 Test Review: Systems of Equations and Inequalities

What is the only method that solving Systems of Equations and Systems of Inequalities have in common?

• Graphing

• Substitution

• Elimination

Consider the following information.

·       Pretzels cost $4.99 per pound

·       Chocolate chips cost $2.99 per pound

·       Sylvie needs a total of 5 pounds of pretzels and chocolate chips for her trail mix.

• She has $30 to spend on ingredients.

If p is the pounds of pretzels and c is the pounds of chocolate chips Sylvie can purchase, which system of equations can be used to model the scenario?

• 2.99p + 4.99c = 30

  p + c = 5

• 4.99p + 2.99c = 5

  p + c = 30

• 4.99p + 2.99c = 30

  p + c = 5

• 2.99p + 4.99c = 5

  p + c = 30

The tables to the left model two equations in a system of equations. Based on the information in the tables, what is the solution to the system of equations being modeled?

• (2.5, 2.5)

• (1, 3)

• (6, 2.5)

• (1.5, 4)

• (3, 2)

• (2, 9)

• (2, 3)

What is the result of the first step if you solve the following system of equations using elimination?

8x + 14y = 4

12x + 14y = 20

• -4x = -16

• 20x = 24

• 20x = -16

• -4x = 24

• No solution

• Infinite solutions

• x = 10, y = 0

• x = 0, y = 10

• (0, 3)

• (-4, 7)

• (4, 7) 
• (4, -5)
• (2, 2)
• (6,0)
• (8, 4)

The graph below shows the boundary lines for the system: y > -1/2x - 2 and y <= -3/2x + 2. Which region contains the solutions to the system?

• Region A

• Region B

• Region C

• Region D

Write the system of inequalities for the scenario below: Your family is at an amusement park and is getting hungry. They have a maximum of $40 to spend on food at a concession stand. It costs $3 per drink and $5 per hamburger. Your family wants to buy no more than 8 items.

• 3d + 5h ≤ 40

  d + h ≤ 8

• 3d + 5h ≥ 40

  d + h ≥ 8

• 3d + 5h ≤ 40

  d + h ≥ 8

• 3d + 5h ≥ 40

  d + h ≤ 8