Chapter 6 Practice Test Questions
The following questions could be used in a Chapter 6 Test
Choose the best answer.
The cost of a phone bill c is divided evenly among 3 roommates. Which expression shows the cost for each roommate?
The day’s high temperature was 10°F and the day’s low temperature was –3°F. What was the difference between the day’s high and low temperatures?
Evaluate
Which root is NOT irrational?
The associative property allows you to rewrite [3 (2 + 9)] • 8 as which expression?
Simplify 8 (x – 5) - x + 2.
Ralph bought one sweater for $19.99 and 3 pairs of socks. In all, he spent $28.96. Assuming there was no sales tax, which equation can be solved to find the price of each pair of socks?
For which equation are there no solutions?
Solve
Solve the formula A = P + Prt for t.
Solve
A manager said the per item profit should be no less than $14. Which graph shows the acceptable profits?
Which describes the solutions of x + 5 < 1?
Solve -2d > 18.
Which graph shows the solutions of 4x - 6 > 2x - 9?
Which solutions are shown by the graph below?
Solve
What is the range of the relation shown?
The park charges $20 plus $5 per hour to rent a boat. Which function gives the total amount charged?
For h(x) = -2x + 7, find f(x) when x = 3.
For which situation would you expect to see no correlation?
The age of a computer and the number of times it crashes.
The number of trees on a property and the number of leaves on the ground.
The height of a person and the number of books they read last year.
The number of chips in a bag and the length of time since it was opened.
Which graph does NOT represent a function?
What are the next three terms in the arithmetic sequence
2.2, 3.7, 5.2, …?
What is the x-intercept of 3x - 5y = 30?
What is the slope of the line that contains (-3, 4) and (7, 5)?
Which equation has the same slope as y = 4x - 5?
Which equation does NOT represent adirect variation?
Which is the equation of a line through (0, 7) with a slope of ˝ ?
Which pair of lines is perpendicular?
Which ordered pair is a solution of x - y = 2 and 3y - x = 8
Solve x + y = 60 and x = 2y - 6
Solve 2x - y = 13 and 3x + y = 12
Which of the following classifications fits the system y = 3x + 4 and
x + 3y = 6
consistent and independent
consistent and dependent
inconsistent and independent
inconsistent and dependent
A pharmacist mixes a solution that is 1% salt with a solution that is 5% salt to make 280 milliliters of solution that is 2% salt. Which system can be used to find how much of each solution is in the mixture?
Which inequality is represented by the graph below?
Which system of linear inequalities is represented by the graph below?
Choose the best answer.
Which inequality is represented by the graph shown?
Which ordered pair is a solution of the system graphed below?
Which is the graph of y _ _2x _ 1?
For which would you draw a dashed boundary line and shade to the left?
Which of the following is a solution of the system graphed below?
Which is true for y > x + 1 and y > x + 3?
The system has no solutions.
The solutions are the points between the two lines.
The solutions are the same as the solutions of y > x + 1.
The solutions are the same as the solutions of y > x + 3.
The drama club is having a car wash as a fundraiser. They wash x cars at $5 each and y trucks at $8 each. They will wash at least 26 cars and 15 trucks. They need to make at least $250. Which system describes this situation?
Choose the best answer.
Which ordered pair is a solution of x = 2y + 1 and y = x ?
The graph of a system of linear equations is shown below. What is the solution of the system?
Solve by substitution: y = x + 1 and x + y = 7
Solve by elimination: 2x + y = 10 and x - y = 2
Leslie joins a fitness club that has a membership fee of $20 plus $15 per month. Rashad’s club has a fee of $40 and charges $10 per month. In how many months will the two clubs cost the same?
Solve by any method: -x + y = 1 and x + y = 3
Which phrase describes a system with exactly one solution?
consistent and independent
consistent and dependent
inconsistent
dependent
Solve x = 2y + 4 and 2y = x - 6
Gabbi paddles her canoe 6 miles downstream (with the current) in 2 hours. Then she paddles 6 miles upstream (against the current) in 6 hours. Which of the following is true?
The solution of which linear inequality is graphed below?
Which ordered pair is a solution of y < x + 1?
The graph of a system of linear inequalities is shown below. Which ordered pair is a solution of the system?
Amber is buying drinks and snacks for a party at her house. She can spend no more than $20. Drinks d cost $1 each. Snacks s cost $2 each. She needs at least 5 drinks and at least 5 snacks. Which system represents this situation?
Choose the best answer.
Which ordered pair is a solution of x - y = -3 and 2x + y = 0?
The graph of a system of linear equations is shown below. What is the solution of the system?
Solve by substitution: y = x + 3 and 2x + y = 9
Solve by elimination: 3x + 2y = 1 and x + 2y = 11
Sam needs to make a long-distance call from a pay phone. With his prepaid phone card, he will be charged $1.00 to connect and $0.50 per minute. If he places a collect call with the operator he will be charged $3.00 to connect and $0.25 per minute. In how many minutes will the phone card and the collect call cost the same?
Solve by any method: 2x + y = 11 and x + 3y = 18
Which term describes a system with no solution?
consistent
dependent
inconsistent
independent
Solve 4x = 2y + 6 and y = 2x - 3
A dermatologist mixes a 10% benzoyl peroxide ointment with a 20% benzoyl peroxide ointment to make 50 grams of an ointment that is 14% benzoyl peroxide. How much of each ointment are mixed together?
The solution of which linear inequality is graphed below?
Which ordered pair is a solution of y > 5x - 2?
The graph of a system of linear inequalities is shown below. Which ordered pair is a solution of the system?
A factory makes widgets x and gadgets y. Widgets cost $3 and gadgets cost $5 each to make. The boss wants at least 10 widgets and 20 gadgets per day. Total costs need to be at most $300 per day. Which system represents this situation?
Choose the best answer.
Which ordered pair is a solution of: 4x - y = -3 and 3y -6x = 6?
Estimate the solution to the system.
Solve by substitution: y = 3x + 2 and 3x - 2y = -13
Solve by elimination: 2x - 3y = -7 and 2y - 4x = 10
Robin has $24.50 and her brother Wayne has $68.50. Wayne is paying Robin $2.75 each day to help with his chores. When will they have the same amount of money?
Solve 2y = 3x + 4 and 3y - 2x = -4
Logan has read 14 books and is reading 1 each week. Mariko has read 12 books and is reading 1 each week. Which term describes this scenario?
consistent
dependent
inconsistent
independent
Solve
The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 24 less than four times the original number. What is the original number?
The solution of which linear inequality is graphed below?
Which ordered
pair is a solution of 
Which ordered pair is a solution of the system?
A class fundraiser is earning $7 per car wash w and $4 per carrot cake c sold. Carrot cakes cost $2 to make and the supplies for the car wash cost $1 per car. They will wash less than 50 cars and bake no more than 30 cakes. They want to raise at least $320 to give to a local charity. Which system represents this situation?
Tell whether (5, 2) is a solution of x + 3y = 11 and 2x - y = 3
Solve y = x - 3 and y = -x + 5 by graphing.
Solve by substitution: y = 10 + x and 2x + y = 4
Solve by elimination: x - 2y = -7 and 4x + 2y = 22
Tank A contains 35 gallons of water and is increasing at a rate of 5 gallons per minute. Tank B contains 100 gallons of water and is decreasing at a rate of 8 gallons per minute. In how many minutes will the tanks contain the same amount of water? How much water will that be?
Solve by any method: y - 3x = 2 and y = -2x – 8
Classify y = -6x + 10 and y = -6x + 3
consistent and independent
consistent and dependent
inconsistent.
Solve y = ˝x + 5 and 2y = x + 10
Paul creates a CD by mixing together songs that are either 3 minutes or 4 minutes long. His CD has 22 songs and is 78 minutes long. How many three-minute and how many four-minute songs did he use?
Write the inequality represented by the graph below.
Tell whether (1, 10) is a solution of and y > 5 + 6x.
Graph 
Give two ordered pairs that are solutions and two ordered pairs that are not solutions.
At Healthy Hair, the cost of a children’s haircut x is $4 and the cost of an adult haircut y is $14. The manager’s goal for the day is to have at least 5 children’s cuts, at least 20 adult cuts, and to have total sales be greater than $500. Write a system to represent this situation.
Tell whether (-5, -6) is a solution of x - 2y = 7 and y - x = -1
Solve 4x + y = -1 and y - 4 = x
Solve by substitution: 3x - 2 = y and y -2x = -5
Solve by elimination: 3x - 2y = 4 and x + 4y = 34
The population of Medford High School is 800 students and the population of Westville High School is 1240 students. The population of Medford High has been increasing at a rate of 30 students per year, while the population of Westville High has been decreasing by 25 students per year. If these rates remain constant, in how many years will the populations of the two schools be the same? How many students will that be?
Solve by any method: y - 5 = -˝x and x = y - 2
Classify y = 2/3x + 7 and 3y = 2x + 21
Solve 8y - 6x = 48 and 2y = 3/2x - 12
The sum of the digits of a two-digit number is 8. When the digits are reversed, the new number is 54 less than the original number. What is the original number?
Write the inequality represented by the graph below.
Tell whether
(4, 3) _ is a solution of 
Graph
Give two ordered pairs that are solutions and two ordered pairs that are not solutions.
A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation.
Tell whether
is
a solution of 2x – y = -2 and y – 4x = 3
Solve
Solve by substitution: -2x - y =3 and y - 12 = x
Solve by elimination: 3y - 4x = 29 and 2y + 5x = 4
A museum projects two copies of an image side-by-side. The left-side image starts at a width of 48 inches and its width narrows 3 in. per min. The right side image starts at a width of 3 inches and its width expands 6 in. per min. How long will it take for the photos to have the same width? What will the width be at that time?
Solve by any
method: 
Classify 5y - 4x = -5 and 10y + 2 = 4x
Solve 6y - 4x = 6 and 9y = 6x + 9
A chemist has a 2% acid solution and an 8% acid solution. He wants to mix the solutions to get 300 mL of a 5.5% acid solution. How many milliliters of each solution does he need?
Write the inequality represented by the graph below.
Tell whether
is
a solution of 
Graph y
- 3x < 5 and 3x - y
7
Give two ordered pairs that are solutions and two ordered pairs that are not solutions.
An artist has 600 inches of framing material to form a rectangular frame. The dimensions of the wall on which it will hang limit the frame’s width to no more than 200 inches. The artist wants the length to be at least 2 times longer than the width. Write a system to represent this situation.
Choose the best answer.
Which ordered pair is the solution of the system graphed below?
What does it mean if (3, 2) is a solution of y = x – 1 and y = -x + 5
Solve y = x + 3 and 2x + y = -6 by substitution.
Which is true about the equations of an inconsistent linear system?
Their slopes are the same, but their y-intercepts are different.
Their slopes are different, but their y-intercepts are the same.
Their slopes are different, and their y-intercepts are different.
Their slopes are the same, and their y-intercepts are the same.
Solve 2x - 3y = -14 and 3x + 3y = 9 by elimination.
How many solutions does the system y = 2x + 1 and -4x + 2y = 2 have?
Joe spent $7.75 to purchase 23 snacks for the club meeting. Veggie chips are $0.25 and pretzels are $0.50. How many of each type of snack did Joe buy?
The sum of the digits of a two-digit number is 10. If the digits are reversed, the number increases by 36. Which system can be used to find the tens digit t and units digit u of the original number?