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System of Linear Equations Word Problems - Printable Mathematics Worksheets - Wayground

System of Linear Equations Word Problems

8 questions

9th Grade

Mathematics

System of Linear Equations Word Problems is a Grade 9 mathematics worksheet with 8 multiple-choice questions. Students translate real-world situations involving ticket prices, food sales, book costs, family meals, and running yards into systems of linear equations. The worksheet also asks students to solve a system by graphing, identify the intersection as the solution, and select equations that correctly represent given totals and relationships. This free printable worksheet helps students connect algebraic representations to practical contexts while checking whether variables, coefficients, and constants match the information in a problem. It is useful for guided practice, independent review, or an assessment of students’ ability to model and interpret systems of equations. A complete answer key is included so teachers can review the selected systems and solutions efficiently.

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System of Linear Equations Word Problems

Total questions: 8

Name
Class
Date
1.

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

2.

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

3.

Solve the following system by graphing.  What is the solution?

a)

Infinite number of solutions

b)

(3, 3)

c)

(3, -3)

d)

(-3, 3)

4.

The solution (x, y) to a system of equations is the point where they...? 

a)

Run off the graph

b)

Don't touch

c)

Intersect

d)

Exist

5.

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. 

a)

35 nachos, 52 sodas

b)

18 nachos, 69 sodas

c)

52 nachos, 35 sodas

d)

61 nachos, 26 sodas

6.

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

7.

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

8.

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

Answer Key

System of Linear Equations Word Problems

Total questions: 8

1.
c)

Van 14
Bus 43

2.
d)

Adult $12
Child $13

3.
b)

(3, 3)

4.
c)

Intersect

5.
a)

35 nachos, 52 sodas

6.
a)

t + n = 54

t = 3n + 8

7.
a)

x + y = 6

14.80x + 17y = 91

8.
a)

x + y = 1550

y = 4x

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FAQs

What does this system of linear equations word problems worksheet cover?

This Grade 9 worksheet uses 8 multiple-choice questions to practice modeling situations with systems of linear equations and interpreting their solutions. Students identify equations for totals and relationships, solve one system by graphing, and recognize that the solution is the point where the graphs intersect.

How can I use this worksheet to teach modeling systems of linear equations?

Have students define the variables and identify the two facts in each scenario before examining the answer choices. For the ticket, food, book, meal, and football-yard problems, ask students to explain which equation represents a total and which represents a price or comparison relationship. Then use the graphing questions to connect the algebraic system to its intersection point.

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

Students may reverse the variables in relationship statements, such as writing the novel price as three times the textbook price, or use a total number where a total cost belongs. They may also confuse the coefficients in the meal and concession problems, overlook the combined-total equation, or choose a graphing answer without identifying the intersection as the solution.

How do I assign and grade this worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app. The printable format can also support schools that want to reduce screen time.

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

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the multi-step word problems and answer choices easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the system-modeling and multiple-choice format.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, including downloadable PDFs and answer keys. Browse more resources at https://wayground.com/en-us/worksheets to help students master essential skills and concepts.

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