Free Printable 5.2 Systems Elimination and Word Problems

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?

a)

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

b)

x + y = 4
x - y = 6

c)

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

d)

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

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?

a)

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

b)

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

c)

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

d)

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

3.

What do you get for y when you start solving

a)

2

b)

-1

c)

1

d)

-2

4.

Solve for x

a)

1

b)

-2

c)

-1

d)

-6

5.

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

a)

x

b)

y

6.

What does the new equation become after multiplying?

a)

-12x + 6y = 26

b)

-12x + 18y = 26

c)

-12x + 18y = 78

7.

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

a)

15 & -15

b)

10 & -10

c)

8 & -8

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?

a)

5x = 25

b)

5x + 10y = 20

c)

5x = 20

d)

6x = 30

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?

a)

3x + 3y = 30

b)

2x = 20

c)

6x = 30

d)

5x = 25

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?

a)

15x = 50

b)

5x = 15

c)

15x + 4y = 50

d)

10x = 30

11.

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.

8x + 9y = −82

-x − 9y = 89

a)

Add to eliminate x

b)

Add to eliminate y

c)

Subtract to eliminate x

d)

Subtract to eliminate y

12.

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.

8x + 9y = -24

-8x − y = 16

a)

Add to eliminate x

b)

Add to eliminate y

c)

Subtract to eliminate x

d)

Subtract to eliminate y

13.

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.

4x + 9y = 1

4x − 7y = 11

a)

Add to eliminate x

b)

Add to eliminate y

c)

Subtract to eliminate x

d)

Subtract to eliminate y

14.

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.

3x + 7y = 14

4x − 7y = 21

a)

Add to eliminate x

b)

Add to eliminate y

c)

Subtract to eliminate x

d)

Subtract to eliminate y

15.

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.

-8x + 6y = 12

-8x − 7y = 1

a)

Add to eliminate x

b)

Add to eliminate y

c)

Subtract to eliminate x

d)

Subtract to eliminate y

16.

4x+8y=20

-4x+2y=-30

a)

(-7,1)

b)

(2,-5)

c)

(-2,5)

d)

(7,-1)

17.

Solve the system by elimination.
−4x − 4y = 0
4x + 4y = 0

a)

(−6, −4)

b)

Infinite number of solutions

c)

(−6, 10)

d)

(6, 4)

18.

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

a)

d + n = 6.60
.10d + .05n = 80

b)

d + n = 80
d + n = 6.60

c)

d + n = 80
.10d + .05n = 6.60

d)

d + n = 80
.05d + .10n = 6.60

19.

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?

a)

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

b)

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

c)

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

d)

x + y = 49
x + y = 1430

20.

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

5x - 2y = 11

-10x + 3y = -4

a)

5

b)

-1

c)

2

d)

-2

21.

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

2x + 3y = 12

4x - 7y = - 54

a)

4x - 6y = -24

b)

-4x - 6y = 12

c)

-4x - 6y = 24

d)

-4x - 6y = -24

22.

What is the solution to this system of equations?

4x + y = 6

x - 2y = 6

a)

(2,-2)

b)

(1,2)

c)

( 1/2 , 4 )

d)

(-2,2)

e)

(2, 4)

23.

Solve the system

2x + 3y = 6

x + 2y = 5

a)

( 4 , -3 )

b)

( -3 , 4 )

c)

( 3 , 4 )

d)

( 4 , 3 )

24.

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

a)

(-1, -1)

b)

(2,-1)

c)

(1,1)

d)

(1,-1)

25.

Parallel Lines never intersect because...

a)

they have the same slopes.

b)

they have the same y-intercept.

c)

they have different slopes.

d)

they have different y-intercepts.

26.

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

a)

(1, -10)

b)

No solution

c)

(-4, 1)

d)

(1, 10)

27.

Solve the following system:

4x - 6y = -6

-2x -12y = -12

a)

(0,1)

b)

(1,0)

c)

(1,1)

d)

(2,1)

28.

Solve the system:

2x + 9y = -7

6x - 3y = 9

a)

(-1, -1)

b)

(2,-1)

c)

(1,1)

d)

(1,-1)

29.

Solve the system:

2x + 10y = -20

-x + 4y = 28

a)

(-20,2)

b)

(1,4)

c)

(2,-20)

d)

(-2,2)

30.

Solve the following system:

5x + 4y = 1

10x + 6y = -6

a)

(-3, 4)

b)

(-3, -4)

c)

(3, 4)

d)

(4, -3)

e)

(4, 3)

31.

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

a)

(6,13)

b)

(19, 4)

c)

(10,4)

d)

(4,0)

32.

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

a)

ADD

b)

SUBTRACT

33.

Use elimination to solve the system of equations.
WRITE YOUR SOLUTION AS AN ORDERED PAIR (x,y).
DO NOT WRITE ANY SPACES.
$2x-3y=-6$
$-5x-9y=15$

(a)

34.

Use elimination to solve the system of equations.
WRITE YOUR SOLUTION AS AN ORDERED PAIR (x,y).
DO NOT WRITE ANY SPACES.
$4x-9y=-11$
$-y+3x=9$

(a)

35.

5x + y = 9
10x − 7y = −18

a)

(4, -11)

b)

(1, 4)

c)

(-1, 14)

d)

(-4, 29)

36.

Solve the following system by using elimination:

-2x - 5y = -15

x + 8y = 13

a)

(5, 1)

b)

(1, 5)

c)

(5, -1)

37.

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?

a)

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

b)

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

c)

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

d)

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

38.

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

a)

(26, 23)

b)

(26, 29)

c)

(29, 26)

d)

(29, 32)

39.

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?

a)

Sugar Cookies $5
Oatmeal Cookies $3

b)

Sugar Cookies $4
Oatmeal Cookies $8

c)

Sugar Cookies $2
Oatmeal Cookies $6

d)

Sugar Cookies $3
Oatmeal Cookies $6

40.

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?

a)

(35, 52)

b)

(18, 69)

c)

( 52, 35)

d)

(61, 26)

41.

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?

a)

Van 43
Bus 14

b)

Van 11
Bus 21

c)

Van 14
Bus 43

d)

Van 17
Bus 45

42.

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.

a)

Adult $13
Child $5

b)

Adult $10
Child $6

c)

Adult $8
Child $16

d)

Adult $12
Child $13

43.

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?

a)

20 Multiple Choice

b)

10 Multiple CHoice

c)

15 Multiple Choice

d)

5 multiple choice

44.

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?

a)

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

b)

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

c)

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

d)

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

45.

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?

a)

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

b)

x + y = 4
x - y = 6

c)

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

d)

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

46.

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?

a)

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

b)

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

c)

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

d)

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

47.

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?

a)

x + y = 1550

y = 4x

b)

x + y = 1550

y = x + 4

c)

y - x = 1550

y = 4x

d)

y = 1550 + x

y = x + 4

48.

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?

a)

t + n = 54

t = 3n + 8

b)

t + n = 54

n = 3t + 8

c)

t + n = 54

t = 3n - 8

d)

t + n = 8

t = 3n + 54

49.

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?

a)

x + y = 6

14.80x + 17y = 91

b)

x + y = 91

14.80x + 17y = 6

c)

x + y = 6

14.80y + 17x = 91

d)

x + y = 91

14.80x+ 17y = 6

50.

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

a)

5q + 2z = 1.32
1z = 0.75

b)

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

c)

q + z = 1.32
q + z = 0.75

d)

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

51.

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?

a)

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

b)

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

c)

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

d)

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

52.

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

a)

y = 6.80 + .65x
y=7.30+.90x

b)

x + y = 6.80
x + y = 7.30

c)

y = 6.80+.90x
y = 7.30 + .65x

d)

y + .90x = 6.80
y + .65x = 7.30

53.

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?

a)

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

b)

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

c)

t: total cost
m: # of food items

d)

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

54.

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?

a)

t + n = 54
t = 3n + 8

b)

t + n = 54
n = 3t + 8

c)

t + n = 54
t = 3n - 8

d)

t + n = 8
t = 3n + 54

55.

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?

a)

(35, 52)

b)

(18, 69)

c)

( 52, 35)

d)

(61, 26)

56.

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?

a)

10 horses, 18 chickens

b)

16 horses, 12 chickens

c)

12 horses, 16 chickens

d)

18 horses, 10 chickens

57.

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?

a)

$5

b)

$10

c)

$15

d)

$20

58.

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?

a)

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

b)

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

c)

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

d)

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

59.

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

a)

(10, 11)

b)

(12, 9)

c)

(11, 10)

d)

(9, 12)

60.

Five less than twice a number is equivalent to 47.

a)

5 - 2x = 47

b)

2x - 5 = 47

c)

5x - 2 = 47

d)

2 - 5x = 47

61.

10 less that half a number is equivalent to 8.

a)

10 - 1⁄2x = 8

b)

1⁄2x + 10 = 8

c)

1⁄2x - 10 = 8

d)

10x - 0.5 = 8

62.

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

a)

3x + 7 = 57

b)

3(x + 7) = 57

c)

7x + 3 = 57

d)

7(x + 3) = 57

63.

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?

a)

x + y = 1550
y = 4x

b)

x + y = 1550
y = x + 4

c)

y - x = 1550
y = 4x

d)

y = 1550 + x
y = x + 4

64.

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

a)

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

b)

x = -2
y = 5

c)

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

d)

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

65.

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?

a)

t + n = 54
t = 3n + 8

b)

t + n = 54
n = 3t + 8

c)

t + n = 54
t = 3n - 8

d)

t + n = 8
t = 3n + 54

66.

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?

a)

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

b)

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

c)

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

d)

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

67.

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?

a)

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

b)

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

c)

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

d)

x + y = 49
x + y = 1430

68.

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?

a)

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

b)

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

c)

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

d)

x + y = 49
x + y = 1430

69.

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

a)

5q + 2z = 1.32
1z = 0.75

b)

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

c)

q + z = 1.32
q + z = 0.75

d)

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

70.

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)?

a)

C = 0.20x + 15

b)

C =15 (0.20x)

c)

C = 15 + x + 0.20

d)

C = 0.20 + 15x

5.2 Systems Elimination and Word Problems

Total questions: 70

Worksheet time: 8hrs 50mins

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