Chapter 3 Review of Systems

Chapter 3 Review of Systems

by Rachel McBride

​A System of Equations

• ​with one solution

• ​contains intersecting lines

• ​is an independent system

​A System of Equations

• with no solutions

• ​contains parallel lines

• ​is an inconsistent system

​A System of Equations

• with infinite solutions

• ​contains coinciding lines

• ​is a dependent system

Multiple Choice

How many solutions does this system of equations have in the given graph?

• One Solution
• No solution
• Infinitely Many Solutions

Multiple Choice

What is the solution to the system of equations graphed below?

• No Solution

• Infinite Solutions

• One Solution: (0, 2)

• One Solution: (2, 6)

Multiple Choice

What is the solution to the system?

• (0, 3)
• (1, -1)
• (-3, 1)
• (1, 3)

Multiple Choice

• (2, -2)
• (2, 2)
• (-2, 2)
• (-2, -2)

Multiple Choice

Which system of inequalities 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 + 3

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Tell whether the ordered pair 
(-3, 0) is a solution of the given system.
y ≤ x + 4
y ≥ 2x - 6

• Yes
• No

​Use the information for the following questions. You may need to write this down

An office building containing 96,000 square feet of space is to be made into apartments. There will be one-bedroom (x) and two-bedroom (y) apartments built using the space.

Multiple Choice

An office building containing 96,000 square feet of space is to be made into apartments. There will be one-bedroom (x) and two-bedroom (y) apartments built using the space.

There will be at most 15 one-bedroom units, each with 800 square feet of space. Write an equation representing the number of one bedroom units.

• $$x\ <\ 15$$  

• $$x\ \le\ 15$$  

• $$x\ >\ 15$$  

• $$x\ \ge\ 15$$  

Multiple Choice

An office building containing 96,000 square feet of space is to be made into apartments. There will be one-bedroom (x) and two-bedroom (y) apartments built using the space. There will be at most 15 one-bedroom units, each with 800 square feet of space.

The remaining units each with 1200 square feet of space will have two-bedrooms. Write an equation representing the number of two-bedroom units.

• $$y>0$$  

• $$y\ \le15$$  

• $$y\ge0$$  

• $$y\ \ge15$$  

Multiple Choice

An office building containing 96,000 square feet of space is to be made into apartments. There will be one-bedroom (x) and two-bedroom (y) apartments built using the space. There will be at most 15 one-bedroom units, each with 800 square feet of space. The remaining units each with 1200 square feet of space will have two-bedrooms.

Write an equation to represent the number of apartments to be built using the square footage.

• $$650x\ +\ 900y\ \le96000$$  

• $$800x\ +\ 1200y\ \ge96000$$  

• $$800y\ +\ 1200x\ \ge96000$$  

• $$800x\ +\ 1200y\ \le96000$$  

Draw

Draw the System of Inequalities

Fill in the Blanks

Find the vertices of the corners

List your answers in (x,y)(x,y)form from the left to the right

Multiple Choice

If the rent for each one-bedroom unit is $650 and for each two-bedroom unit is $900. Which of the following represents the objective function

• 650x + 900y

• 900x + 650x

• 650(x -y) + 900

• 650x - 900y

Multiple Choice

If the rent for each one-bedroom unit is $650 and for each two-bedroom unit is $900. How many of each will maximize the revenue?

• x = 15

  y = 70

• x = 70

  y = 15

• x = 0

  y = 80

• x = 120

  y = 0

Fill in the Blanks

What is the maximum revenue?

Multiple Choice

A glass blower can form 8 simple vases or 2 elaborate vases in an hour. In a work shift of no more than 8 hours, the worker must form at least 40 vases. Let s rerepsent the hours forming simple vases and e represent the hours forming elaboarte vases. Write the system of equations involving the time spent per hour.

• $$s\ +e\le8$$  

• $$8s\ +2e\le8$$  

• $$s\ +e\le40$$  

• $$8s\ +2e\le40$$  

Multiple Choice

A glass blower can form 8 simple vases or 2 elaborate vases in an hour. In a work shift of no more than 8 hours, the worker must form at least 40 vases. Let s rerepsent the hours forming simple vases and e represent the hours forming elaboarte vases. Write the system of inequalities involving the time spent on each type of vase.

• $$s\ +e\ge8$$  

• $$8s\ +2e\ge8$$  

• $$s\ +e\ge40$$  

• $$8s\ +2e\ge40$$  

Fill in the Blanks

If the glass blower makes a profit of $30 per hour worked on a the simple vases (s) and $35 per hour worked on the elaborate vases (e), write a function for the total profit on the vases.

Multiple Choice

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

• x + y ≤ 8
• x + y ≤ 6
• 2x + 3y ≤ 6
• x + y ≤ 10

Multiple Choice

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18
• x + y ≤ 6
• x + y ≤ 9
• 3x + 2y ≤ 18

Multiple Choice

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective quantity?

• P = 30x + 50y
• P = 50x + 30y

Multiple Choice

Objective quantity:
P = 30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

• 300
• 280
• 400
• 240

Multiple Choice

Which are vertices of the feasible region?

• (0, 3) (3, 0) (5, 8)

• (0, 6) (3, 5) (6, 5)

• (3, 3) (8, 5) (5, 8)

• (0, 5) (6, 0) (3, 3)

Multiple Choice

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