Deck 3: When Lines Meet: Linear Systems

Question 1

Determine whether is a solution to the following system.

A) It is not a solution.
B) It is a solution.

Answer 1

It is a solution.

Question 2

Determine whether is a solution to the following system.

A) It is not a solution.
B) It is a solution.

Answer 2

It is not a solution.

Question 3

Determine whether is a solution to the following system.

A) It is not a solution.
B) It is a solution.

Answer 3

It is a solution.

Question 4

Determine whether is a solution to the following system.

A) It is a solution.
B) It is not a solution.

Question 5

Estimate the solution of the system pictured.

A)
B)
C)
D) and

Question 6

Estimate the solution of the system of equations pictured.

Question 7

Estimate the solutions of the system of equations pictured.

Question 8

Estimate the solutions of the system of equations pictured.

Question 9

From the graph shown, identify where y1 < y2. Give your answer in interval form.

Question 10

From the graph shown, identify where y1 > y2. Give your answer in interval form.

Question 11

Solve this system of equations by sketching the graphs and estimating the solution.
5x + y = -8
3x - 4y = 9

Question 12

The following graph represents the annual operating expenses and the annual sales (both in $1,000s) for a new graphics business.

In what year did sales finally equal expenses?

Question 13

Determine which ordered pairs are solutions to the system of equation.
3x + 3y = 9
-2x - 4y = -8

A) (2, -1)
B) (-2, 1)
C) (2, 1)
D) (2, 2)

Question 14

Franklin Meadows is considering opening a lumber business. He estimates that his total expenses will be represented by the formula M_expenses = 17.1 + 3.8x and that his total sales will be estimated by the formula M_sales = 11.4x - 28.5. (Where x is the number of years the business has been operating and M is in $1,000s.) How many years will it take for Franklin's sales to equal his expenses?

Question 15

Victoria has been hired by C&M sales to be an account representative. She has been offered two salary options. Option A has a base pay of $880 per week with a commission of $26 for every thousand dollars in sales. Option B has a base pay of $160 per week with a commission of $42 for every thousand dollars in sales. How many thousands of dollars in sales would Victoria need to reach each week in order for the two options to be equal?

Question 16

Solve the system by graphing.

Question 17

Solve the system by elimination.

Question 18

Solve the system by elimination.

Question 19

Solve the system by elimination.

Question 20

Solve the system by elimination.

Question 21

Solve the system by elimination.

Question 22

Solve the system by substitution.

Question 23

Solve the system by substitution.

Question 24

Solve the system by substitution.

Question 25

Solve the system by substitution.

Question 26

Solve the system.

Question 27

Solve the system.

Question 28

Solve the system.

Question 29

Solve the system.

If the system is either inconsistent or dependent, enter either inconsistent or dependent.

Question 30

Solve the system.

If the system is either inconsistent or dependent, enter either inconsistent or dependent.

Question 31

Solve the system of equations.

If the system is either inconsistent or dependent, enter either inconsistent or dependent.

Question 32

Solve the system.

If the system is either inconsistent or dependent, enter either inconsistent or dependent.

Question 33

Determine the number of solutions of the system.

A) zero
B) an infinite number
C) one
D) two

Question 34

Determine the number of solutions of the system.

A) one
B) an infinite number
C) zero
D) two

Question 35

A shopkeeper has two types of coffee beans on hand. One type sells for $3.20 per lb, the other for $6.00 per lb. How many pounds of the $3.20 per lb coffee beans must be used in the mixture to produce 55 lbs of a blend that sells for $3.62 per lb?
Round your answer to 2 decimal places.

Question 36

AAA Car Rental charges $44 per day plus $0.15 for each mile driven. CCC Car Rental charges $29 per day plus $0.2 per mile driven.

A) Write a linear function that gives the cost, C, to rent a car for one day from AAA Car Rental as a function the number of miles driven, m.
B) Write a linear function that gives the cost, C, to rent a car for one day from CCC Car Rental as a function the number of miles driven, m.
C) How many miles must you drive in one day before AAA Car Rental is your better choice?

Question 37

A company assumes a linear relationship exists between the consumer demand for its product and the price charged, p.
When the price of its product was $4 per unit, the weekly quantity demanded was 302 units, and when the unit price was raised to $5, the weekly quantity demanded dropped to 296 units.

A) Write a formula for D, the weekly quantity demanded for the product when the price per unit is p dollars.
B) Suppose also that there is a linear relationship between the quantity supplied S of the product and the unit price. p. Suppose that the weekly quantity supplied is 254 when the price is $5 and that the quantity supplied rises by 8.4 units when the price rises by $1.4. Write a formula for S, the weekly quantity supplied when the price of the product is p dollars.
C) The market clearing price or equilibrium point is the price at which supply equals demand. Find the market clearing price for the product.

Question 38

State whether the system of equations illustrated by each graph has "One solution", "No solution", or "Infinitely many solutions".

Question 39

State whether the system of equations has "One solution", "No solution", or "Infinitely many solutions".
-3x + y = 11
-2x + 3y = 12

Question 40

Solve the system of equations. Express the answers in fraction form if necessary.

Question 41

Solve the system of equations. Express the answers in decimal form if necessary.
2.1x + 3.1y = 8.2
4x - 2.7y = -18.8

Question 42

Solve the system of equations by substitution.
y = 3x + 2z - 7
x = -4y 4
-5 = 2x + 2y - z

Question 43

Solve the system of equations using elimination.
3x + 2y - 3z = 15
2x - 3y + 4z = -15
2x - 3y - 2z = -3

Question 44

Matwirth wants to invest a total of $30,000 into two investments. The first investment pays 3% interest, and the second investment pays 4.5% interest. If after 1 years, he wants the total interest from both investments to be $1,185, how much should he invest in each account?

Question 45

A large freight truck leaves the terminal at 8:00 a.m. on a cross-country run. At 9:00 a.m., it is discovered that one package was left behind at the terminal. A small truck leaves the terminal at 9:00 a.m. to catch the large truck. If the large truck is moving at 60 miles per hour and the small truck travels at 70 miles per hour, how long (in hours) will it take the small truck to catch the large truck?

Question 46

A homeowner wishes to have a ramp built to the door of her house. If the ground slopes up at a rate of 1 foot of rise for every 12 feet of run, and the ramp is to slope down at a rate of 1 foot of drop for every 15 feet of run, how far away from the house does the ramp need to start in order to reach a door that is 4.5 feet from the ground?

Question 47

The ski club wishes to raise money for this year's ski competitions. The club decides to sell shorts and t-shirts with the ski team logo for $12 for a pair of shorts and $13 for a t-shirt. At the end of the fundraiser, 166 items had been sold and a total of $2078 had been raised for the club. How many of each item were sold?

Question 48

A company produces a product that sells for $ 22, giving them a revenue of when x units are produced and sold. They have fixed costs of $ 364 and variable costs of $ 18 per unit.

A) Find a formula for their total cost, C, as a function of the number of units produced and sold, x.
B) Find their breakeven point.

Question 49

Determine whether is a solution to the following system.

A) It is not a solution.
B) It is a solution.

Question 50

Determine whether is a solution to the following system.

A) It is not a solution.
B) It is a solution.

Question 51

Determine whether is a solution to the following system.

A) It is not a solution.
B) It is a solution.

Question 52

Determine whether is a solution to the following system.

A) It is a solution.
B) It is not a solution.

Question 53

On the grid provided, graph and shade in the areas described by the linear inequality:
‪

Question 54

Use an inequality to describe the shaded region.

Question 55

Select an inequality to describe the shaded region.

A) y < 2x 2
B) y < 2x 2
C) y > 2x 2
D) y < -2x 2

Question 56

Select an inequality to describe the shaded region.

A) y > x 1
B) y < x 1
C) y < x 1
D) y < x 1

Question 57

Create an inequality to describe the shaded region.

Question 58

On the grid provided, graph and shade in the areas described by the linear inequality:

Question 59

Select an inequality to describe the shaded region.

A)
B)
C)
D)

Question 60

Create an inequality to describe the shaded region.

Question 61

On the grid provided, graph and shade in the areas described by the linear inequality:

Question 62

On the grid provided, graph and shade in the areas described by the linear inequality:

Question 63

On the grid provided, graph and shade in the areas described by the linear inequality:
y > -3

Question 64

On the grid provided, graph and shade in the areas described by the linear inequality:
x < 3

Question 65

On the grid provided, graph and shade in the areas described by the compound inequality:

Question 66

Create a compound inequality to describe the shaded region on the graph:

Question 67

The Wisconsin Agricultural Extension office publishes recommendations for farmers. A recent publication stated that dairy cows should be fed corn (C) according to their production (P) of milk, with the minimum amount of corn being given by the equation C_min = 0.33P + 5 and the maximum amount of corn being C_max = 0.39P + 7. According to this recommendation, what would be the maximum amount of corn that should be fed to a cow that is producing 67 pounds of milk?

Question 68

The Wisconsin Agricultural Extension office publishes recommendations for farmers. A recent publication stated that dairy cows should be fed corn (C) according to their production (P) of milk, with the minimum amount of corn being given by the equation C_min = 0.36P + 5 and the maximum amount of corn being C_max = 0.39P + 7. Create a system of inequalities to describe the recommendation.

Question 69

The safe capacity (in pounds) of a portable propane tank is given by the formula: C_max = 19 - 0.012T. Where T is the current temperature. When the temperature is 41°, is it safe to fill the tank to a capacity of 19.29 pounds?

Question 70

Evaluate the piecewise function.

Evaluate

Question 71

Choose the graph that best fits the function.

A)

B)

C)

D)

Question 72

Use the graph to find the value for each unknown (A, B, C, D, and E) in the function.

Question 73

In a typical overtime pay scheme workers are paid at a fixed hourly rate for the first 40 hours they work, and for any hours beyond 40 they are paid at 1.5 times their hourly rate. For example, a worker who makes $16 per hour and works 45 hours, 5 of which are overtime at 1.5 x 16 = $24 per hour, will make:
(16$/hr x 40 hr) + (24 $/hr x 5 hr) = $640 + $120 = $760
Complete the function that describes the pay, P, for a worker making $10 as a function of the hours worked, h, for up to 60 hours by finding the unknown values (A, B, C, D, and E) in the function,

Question 74

Use the appropriate Tax Rate Schedule below to answer the questions.
Schedule Z-A - Use if your filing status is married filing jointly

Schedule Z-B - Use if your filing status is single

A) Find the taxed owed by someone whose filing status is married filing jointly and whose taxable income is $203,500.
B) Find how much more or less this taxpayer would pay with a flat tax of 18%. If the 18% flat tax is less enter your answer as negative.Round answers to 2 decimal places.

Question 75

Use the appropriate Tax Rate Schedule below to answer the questions.
Schedule Z-A - Use if your filing status is married filing jointly

Schedule Z-B - Use if your filing status is single
A) Find the taxed owed by someone whose filing status is single and whose taxable income is $48,000.
B) Find how much more or less this taxpayer would pay with a flat tax of 20%. If less enter your answer as negative.Round answers to 2 decimal places.

Question 76

Schiel Construction and Excavating charges a destination fee of $150 plus $80 per hour for jobs that take less than 3 hours. For jobs that take 3 or more hours, but less than 8 hours, the destination fee is $125 and the hourly charge is $75. For jobs taking 8 hours or more, the charge is simply $70 per hour. Create a peicewise function to describe the charge for a job.

Question 77

Schiel Construction and Excavating charges a destination fee of $200 plus $80 per hour for jobs that take less than 3 hours. For jobs that take 3 or more hours, but less than 8 hours, the destination fee is $175 and the hourly charge is $75. For jobs taking 8 hours or more, the charge is simply $70 per hour. What the charge be for a job that takes 18 hours?

Question 78

Create a piecewise function to describe the following graph.

Question 79

Create a graph for the piecewise function.

Question 80

Create a piecewise function to describe the following graph.