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System Of Equation Word Problems - Printable Mathematics Worksheets - Wayground

System Of Equation Word Problems

20 questions

8th - 8th Grade

Mathematics

System Of Equation Word Problems is a Grade 8 mathematics worksheet that develops students’ ability to translate real-world situations into systems of two linear equations. Across 20 multiple-choice questions, students identify variables, write equations from quantities and costs, select suitable systems, and interpret solutions involving animals, tickets, prices, coins, transportation, wages, and fees. The worksheet also asks students to determine unknown values from paired conditions, recognize equivalent relationships, and identify standard methods for solving systems, including substitution, elimination, and graphing. It is a free printable worksheet with a complete answer key, suitable for guided practice, independent work, review, or formative assessment after students have learned how systems model two related quantities.

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Worksheets

System Of Equation Word Problems

Total questions: 20

Name
Class
Date
1.

There are 15 animals in a barn.  These animals are horses (x) and chickens (y).  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
2.

Nancy went to the grocery story.  On Monday she purchased 4 apples (x) and 6 bananas (y) 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
3.

Habiba sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Ruth 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
4.
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)
5.

The senior class at Orchard Collegiate High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Essex 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
6.
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
7.
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
8.
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
9.

Yazzy 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 Yazzy 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
10.

On Monday Jay 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
11.
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
12.

Dishann 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
13.

At a corner store the cost for a bag of Takis and a beverage is $2.10. The cost for 2 bags and 3 bev's is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables? 

a)

t: # of bags of Takis b: # of beverages

b)

t: Cost of each bag of Taki's b: Cost of each beverage

c)

t: total cost b: # of food items

d)

t: Cost of each beverage. b: Cost of each bag of Takis

14.
Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount? 
a)
y = 9.65 + x
y = 8.40 + x
b)
y = 9.65x + 43
y = 8.40x + 58
c)
y =9.65x
y = 8.40x
d)
y = 9.65x - 43
y = 8.40x - 58
15.

Which of the following is not a method for solving systems of equations

a)

Elimination

b)

Substitution

c)

Estimation

d)

Graphing

16.

The sum of two numbers is 6. The difference of the two numbers is 46. Find the numbers.

a)

46 and 52

b)

-52 and 40

c)

-26 and 20

d)

-46 and 40

17.
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.  How many nickels and dimes did Dennis earn? 
a)
40 nickels, 40 dimes
b)
52 nickels, 28 dimes
c)
28 nickels, 52 dimes
d)
30 nickels, 50 dimes
18.
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
19.

What would be the first step in finding the solution using elimination?

2x + 2y = -2

3x - 2y = 12

a)

you cannot solve this using eliminiation

b)

cross out the 2x and 3x

c)

cross out the 2y and -2y

d)

change to slope intercept form and graph

20.
Solve for x and y
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
Answer Key

System Of Equation Word Problems

Total questions: 20

1.
a) x + y = 15
4x + 2y = 44
2.
c) 4x + 6y = 13
3x + 7y = 13.5
3.
b) Sugar Cookies $4
Oatmeal Cookies $8
4.
a) (35, 52)
5.
c) Van 14
Bus 43
6.
d) Adult $12
Child $13
7.
d) 5 multiple choice
8.
a) S + A = 530
3S + 4A = 1740
9.
c) x + y = 49
20x + 50y = 1430
10.
b) 10c + 5d = 16.50
5c + 10d = 14.25
11.
a) x + y = 1550
y  = 4x
12.
c) d + n = 80
.10d + .05n = 6.60
13.
b)

t: Cost of each bag of Taki's b: Cost of each beverage

14.
b) y = 9.65x + 43
y = 8.40x + 58
15.
c)

Estimation

16.
c)

-26 and 20

17.
c) 28 nickels, 52 dimes
18.
b) $10
19.
c)

cross out the 2y and -2y

20.
a) (1,3)

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FAQs

What does this worksheet cover?

This Grade 8 worksheet covers translating real-world word problems into systems of two linear equations and using those systems to identify unknown values. Its 20 multiple-choice items ask students to define variables, represent totals and costs with equations, choose the correct system, and solve situations involving tickets, prices, coins, vehicles, and other paired quantities.

How can I use this worksheet to teach writing systems of equations from word problems?

Use the worksheet after introducing a consistent modeling routine: define each variable, identify the total-quantity relationship, identify the value or cost relationship, and then check whether each equation matches the wording. Begin with representation items such as the animal, grocery, ticket, and bill scenarios, then use questions that require finding prices or amounts to discuss how the completed system answers the situation.

What mistakes should I watch for when students complete this systems of equations worksheet?

Watch for students reversing the variables, confusing the total number of items with the total value, or omitting a coefficient such as the four legs per horse or the price of each ticket. Students may also place a fee incorrectly in a linear cost equation, mistake a relationship such as “four times as many” for an addition statement, or select equations that use the right numbers but assign them to the wrong situation.

How do I assign and grade this worksheet?

You can assign System Of Equation Word Problems as a printable PDF or as a digital quiz on Wayground. The worksheet includes a complete answer key for checking the 20 multiple-choice responses, and printable student work can be graded by scanning it with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time.

How can I differentiate this systems of equations worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or increase the font size to make the equations and multiple-choice options easier to scan. You can also apply a dyslexia-friendly font or translate the worksheet into another language, which may help students access the word-problem contexts and mathematical vocabulary.

Where can I find more free worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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