Quiz about 5.2 Systems Elimination and Word Problems

Question 1

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

Accepted Answer

4x + 6y = 13
3x + 7y = 13.5

Answer

4x + 6y = 3
13.5x - 13y = 6

Answer

x + y = 4
x - y = 6

Answer

4x - 6y = 13
3x - 7y = 13.5

Question 2

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

Accepted Answer

S + A = 530
3S + 4A = 1740

Answer

S + A = 530
4S + 3A = 1740

Answer

S + A = 1740
3S + 4A = 530

Answer

S + A = 1740
4S + 3A = 530

Question 3

What do you get for y when you start solving

Accepted Answer

-2

Answer

2

Answer

-1

Answer

1

Question 4

Solve for x

Accepted Answer

-1

Answer

1

Answer

-2

Answer

-6

Question 5

Which variable would be the BEST choice to try and eliminate?

Accepted Answer

x

Answer

y

Question 6

What does the new equation become after multiplying?

Accepted Answer

-12x + 18y = 78

Answer

-12x + 6y = 26

Answer

-12x + 18y = 26

Question 7

What should we try and get the coefficients of y to be?

Accepted Answer

10 & -10

Answer

15 & -15

Answer

8 & -8

Question 8

When using the elimination method to solve the system of equations 2x + 5y = 10 and 3x - 5y = 15, what is the resulting equation after the first step?

Accepted Answer

5x = 25

Answer

5x + 10y = 20

Answer

5x = 20

Answer

6x = 30

Question 9

When using the elimination method to solve the system of equations 4x + 3y = 20 and 2x - 3y = 10, what is the resulting equation after the first step?

Accepted Answer

6x = 30

Answer

3x + 3y = 30

Answer

2x = 20

Answer

5x = 25

Question 10

When applying the elimination method to the system of equations 5x - 2y = 10 and 10x + 2y = 40, what is the resulting equation after the first step?

Accepted Answer

15x = 50

Answer

5x = 15

Answer

15x + 4y = 50

Answer

10x = 30

Question 11

4x+8y=20

-4x+2y=-30

Accepted Answer

(7,-1)

Answer

(-7,1)

Answer

(2,-5)

Answer

(-2,5)

Question 12

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

Accepted Answer

x + y = 49
20x + 50y = 1430

Answer

x + y = 1430
20x + 50y = 49

Answer

x + y = 49
10x + 5y = 1430

Answer

x + y = 49
x + y = 1430

Question 13

what do you need to multiply the top equation by to make a zero pair:

5x - 2y = 11

-10x + 3y = -4

Accepted Answer

2

Answer

5

Answer

-1

Answer

-2

Question 14

Let's multiply the top equation by -2. What would be our new equation?

2x + 3y = 12

4x - 7y = - 54

Accepted Answer

-4x - 6y = -24

Answer

4x - 6y = -24

Answer

-4x - 6y = 12

Answer

-4x - 6y = 24

Question 15

What is the solution to this system of equations?

4x + y = 6

x - 2y = 6

Accepted Answer

(2,-2)

Answer

(1,2)

Answer

( 1/2 , 4 )

Answer

(-2,2)

Answer

(2, 4)

Question 16

Solve the system

2x + 3y = 6

x + 2y = 5

Accepted Answer

( -3 , 4 )

Answer

( 4 , -3 )

Answer

( 3 , 4 )

Answer

( 4 , 3 )

Question 17

Solve by elimination
2x + 9y = -7
6x - 3y = 9

Accepted Answer

(1,-1)

Answer

(-1, -1)

Answer

(2,-1)

Answer

(1,1)

Question 18

Parallel Lines never intersect because...

Accepted Answer

they have the same slopes.

Answer

they have the same y-intercept.

Answer

they have different slopes.

Answer

they have different y-intercepts.

Question 19

Solve the system by elimination.
5x + 8y = -12
3x + 5y = -7

Accepted Answer

(-4, 1)

Answer

(1, -10)

Answer

No solution

Answer

(1, 10)

Question 20

Solve the following system:

4x - 6y = -6

-2x -12y = -12

Accepted Answer

(0,1)

Answer

(1,0)

Answer

(1,1)

Answer

(2,1)

Question 21

Solve the system:

2x + 9y = -7

6x - 3y = 9

Accepted Answer

(1,-1)

Answer

(-1, -1)

Answer

(2,-1)

Answer

(1,1)

Question 22

Solve the system:

2x + 10y = -20

-x + 4y = 28

Accepted Answer

(-20,2)

Answer

(1,4)

Answer

(2,-20)

Answer

(-2,2)

Question 23

Solve the following system:

5x + 4y = 1

10x + 6y = -6

Accepted Answer

(-3, 4)

Answer

(-3, -4)

Answer

(3, 4)

Answer

(4, -3)

Answer

(4, 3)

Question 24

What ordered pair is a solution of 2y - 3x = 8

Accepted Answer

(6,13)

Answer

(19, 4)

Answer

(10,4)

Answer

(4,0)

Question 25

Would you add or subtract the equations to Eliminate a variable?

Accepted Answer

SUBTRACT

Answer

ADD

Question 26

Solve the following system by using elimination:

-2x - 5y = -15

x + 8y = 13

Accepted Answer

(5, 1)

Answer

(1, 5)

Answer

(5, -1)

Question 27

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

Accepted Answer

x + y = 15
4x + 2y = 44

Answer

4x + 2y = 15
x + y = 44

Answer

x = 2y + 44
4x = y + 15

Answer

2x - 4y = 44
x - y = 15

Question 28

The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3.
Solve:
x + y = 55
x - y = 3

Accepted Answer

(29, 26)

Answer

(26, 23)

Answer

(26, 29)

Answer

(29, 32)

Question 29

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

Accepted Answer

Sugar Cookies $4
Oatmeal Cookies $8

Answer

Sugar Cookies $5
Oatmeal Cookies $3

Answer

Sugar Cookies $2
Oatmeal Cookies $6

Answer

Sugar Cookies $3
Oatmeal Cookies $6

Question 30

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

Accepted Answer

(35, 52)

Answer

(18, 69)

Answer

( 52, 35)

Answer

(61, 26)

Question 31

The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. How many students were on each van and each bus?

Accepted Answer

Van 14
Bus 43

Answer

Van 43
Bus 14

Answer

Van 11
Bus 21

Answer

Van 17
Bus 45

Question 32

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.

Accepted Answer

Adult $12
Child $13

Answer

Adult $13
Child $5

Answer

Adult $10
Child $6

Answer

Adult $8
Child $16

Question 33

A test has twenty questions worth 100 points.  The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each.  How many multiple choice questions are on the test?

Accepted Answer

5 multiple choice

Answer

20 Multiple Choice

Answer

10 Multiple CHoice

Answer

15 Multiple Choice

Question 34

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

Accepted Answer

x + y = 15
4x + 2y = 44

Answer

4x + 2y = 15
x + y = 44

Answer

x = 2y + 44
4x = y + 15

Answer

2x - 4y = 44
x - y = 15

Question 35

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

Accepted Answer

4x + 6y = 13
3x + 7y = 13.5

Answer

4x + 6y = 3
13.5x - 13y = 6

Answer

x + y = 4
x - y = 6

Answer

4x - 6y = 13
3x - 7y = 13.5

Question 36

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

Accepted Answer

S + A = 530
3S + 4A = 1740

Answer

S + A = 530
4S + 3A = 1740

Answer

S + A = 1740
3S + 4A = 530

Answer

S + A = 1740
4S + 3A = 530

Question 37

Last season two running backs on the WCHS football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

Accepted Answer

x + y = 1550

y = 4x

Answer

x + y = 1550

y = x + 4

Answer

y - x = 1550

y = 4x

Answer

y = 1550 + x

y = x + 4

Question 38

At the Wayne County bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

Accepted Answer

t + n = 54

t = 3n + 8

Answer

t + n = 54

n = 3t + 8

Answer

t + n = 54

t = 3n - 8

Answer

t + n = 8

t = 3n + 54

Question 39

Your family goes to Mississippi Fried for dinner. There are 6 people in your family. Some order the chicken fingers for $14.80, and some order the Deluxe Chicken Dinner for $17. If the total bill was $91, which system best represents the situation?

Accepted Answer

x + y = 6

14.80x + 17y = 91

Answer

x + y = 91

14.80x + 17y = 6

Answer

x + y = 6

14.80y + 17x = 91

Answer

x + y = 91

14.80x+ 17y = 6

Question 40

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

Accepted Answer

5q + 2z = 1.32
3q + 1z = 0.75

Answer

5q + 2z = 1.32
1z = 0.75

Answer

q + z = 1.32
q + z = 0.75

Answer

5q + 2z = 0.75
3q + 1z = 1.32

Question 41

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

Accepted Answer

10c + 5d = 16.50
5c + 10d = 14.25

Answer

10c + 5d = 14.25
5c + 10d = 16.50

Answer

c + d = 10
5c + 10d = 16.50

Answer

c + d = 5
5c + 10d = 16.50

Question 42

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

Accepted Answer

t: Cost of each taco
m: Cost of each glass of milk

Answer

t: # of tacos
m: # of glasses of milk

Answer

t: total cost
m: # of food items

Answer

t: Cost of each glass of milk
m: Cost of each taco

Question 43

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

Accepted Answer

t + n = 54
t = 3n + 8

Answer

t + n = 54
n = 3t + 8

Answer

t + n = 54
t = 3n - 8

Answer

t + n = 8
t = 3n + 54

Question 44

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

Accepted Answer

(35, 52)

Answer

(18, 69)

Answer

( 52, 35)

Answer

(61, 26)

Question 45

In a pasture, there are horses and chickens. If there are a total of 28 animals and 80 legs, how many chickens and horses are there?

Accepted Answer

12 horses, 16 chickens

Answer

10 horses, 18 chickens

Answer

16 horses, 12 chickens

Answer

18 horses, 10 chickens

Question 46

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

Accepted Answer

$10

Answer

$5

Answer

$15

Answer

$20

Question 47

A local fish market is selling fish and lobsters by the pound. The fish costs $5.25 a pound, while the lobster costs $10.50 a pound. The fish market sells 28.5 pounds and makes $215.25?

Accepted Answer

The market sold 16 pounds of fish and 12.5 pounds of lobster.

Answer

The market sold 18 pounds of fish and 10.5 pounds of lobster.

Answer

The market sold 12.5 pounds of fish and 16 pounds of lobster.

Answer

The market sold 10.5 pounds of fish and 18 pounds of lobster.

Question 48

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:
x + y = 21
6x + 4y = 104

Accepted Answer

(10, 11)

Answer

(12, 9)

Answer

(11, 10)

Answer

(9, 12)

Question 49

Five less than twice a number is equivalent to 47.

Accepted Answer

2x - 5 = 47

Answer

5 - 2x = 47

Answer

5x - 2 = 47

Answer

2 - 5x = 47

Question 50

Three times the sum of a number and 7 is equivalent to 57.

Accepted Answer

3(x + 7) = 57

Answer

3x + 7 = 57

Answer

7x + 3 = 57

Answer

7(x + 3) = 57

Question 51

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

Accepted Answer

x + y = 1550
y = 4x

Answer

x + y = 1550
y = x + 4

Answer

y - x = 1550
y = 4x

Answer

y = 1550 + x
y = x + 4

Question 52

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

Accepted Answer

x + y = -10
x - y = -2

Answer

x - y = -10
x + y = -2

Answer

x = -2
y = 5

Answer

x + y = -2
x - y = -10

Question 53

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

Accepted Answer

t + n = 54
t = 3n + 8

Answer

t + n = 54
n = 3t + 8

Answer

t + n = 54
t = 3n - 8

Answer

t + n = 8
t = 3n + 54

Question 54

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation?

Accepted Answer

x + y = 6
14.80x + 17y = 91

Answer

x + y = 91
14.80x + 17y = 6

Answer

x + y = 6
14.80y + 17x = 91

Answer

x + y = 91
14.80x+ 17y = 6

Question 55

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

Accepted Answer

x + y = 49
20x + 50y = 1430

Answer

x + y = 1430
20x + 50y = 49

Answer

x + y = 49
10x + 5y = 1430

Answer

x + y = 49
x + y = 1430

Question 56

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

Accepted Answer

x + y = 49
20x + 50y = 1430

Answer

x + y = 1430
20x + 50y = 49

Answer

x + y = 49
10x + 5y = 1430

Answer

x + y = 49
x + y = 1430

Question 57

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

Accepted Answer

5q + 2z = 1.32
3q + 1z = 0.75

Answer

5q + 2z = 1.32
1z = 0.75

Answer

q + z = 1.32
q + z = 0.75

Answer

5q + 2z = 0.75
3q + 1z = 1.32

Question 58

The Roaming Cell Phone Company charges $15.00 per month plus $0.20 per minute of airtime usage.  If Juanita uses x minutes of airtime, what is an equation that can be used to determine her monthly cell phone bill (C)?

Accepted Answer

C = 0.20x + 15

Answer

C =15 (0.20x)

Answer

C = 15 + x + 0.20

Answer

C = 0.20 + 15x

5.2 Systems Elimination and Word Problems

70 questions

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

What do you get for y when you start solving

Solve for x

Which variable would be the BEST choice to try and eliminate?

What does the new equation become after multiplying?

What should we try and get the coefficients of y to be?

When using the elimination method to solve the system of equations 2x + 5y = 10 and 3x - 5y = 15, what is the resulting equation after the first step?

When using the elimination method to solve the system of equations 4x + 3y = 20 and 2x - 3y = 10, what is the resulting equation after the first step?

When applying the elimination method to the system of equations 5x - 2y = 10 and 10x + 2y = 40, what is the resulting equation after the first step?

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