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

Solving System of Equations Word Problems

14 questions

9th - 9th Grade

Mathematics

This Grade 9 mathematics worksheet develops students’ ability to model and solve systems of two linear equations in real-world situations. Across 14 multiple-choice questions, students translate ticket sales, concession purchases, animal counts, restaurant bills, currency totals, and movie sales into systems, then identify solutions using substitution or elimination. Several items ask students to find a specific coordinate or variable value rather than the full ordered pair. Use this free printable worksheet to reinforce algebraic modeling after direct instruction, provide independent practice, or check whether students can connect quantities, prices, totals, and variables correctly. The mix of representation and solution questions helps reveal whether students understand both how a system is formed and how it is solved. A complete answer key is included for efficient review and grading.

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Worksheets

Solving System of Equations Word Problems

Total questions: 14

Name
Class
Date
1.
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. Write a system to represent this situation assuming "a" represents # of adult tickets and "c" represents # of children's tickets.
a)
x + y = 21
6x + 4y = 104
b)
x + y = 104
6x + 4y = 21
c)
x + y = 21
6y + 4x = 104
d)
x + y = 104
6x + 4y = 21
2.
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)
3.
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)
1.5x + 0.5y = 78.5
x + y = 87
b)
1.5x + 0.5y = 78.5
1.5x + 0.5y = 87
c)
x + y = 78.5
1.5x + 0.5y = 87
d)
x + y = 78.5
x + y = 87
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.
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
6.
What is the solution to this system of linear equations? 
Use substitution.

y = -2x - 6
-2x + y = 6
a)
(0, -3)
b)
(-3, -12)
c)
(-3, 0)
d)
(3, -12)
7.
What is the value of x in the solutiont o this system of linear equations?
Use substitution.

y = -3x + 3
- 2x + 2y  = 6
a)
0
b)
No solution
c)
4
d)
- 4
8.
What is the solution to this system of linear equations?  
Use substitution.

 y = 4x + 6
5x + y  = -21
a)
(27, 108)
b)
(-3, -6)
c)
(3, 18)
d)
(-3, 6)
9.
What is the solution to this system of linear equations?
Use elimination.

2x + y = 17
   x + y = 10
a)
(7, 5)
b)
(9, -1)
c)
(-1, 9)
d)
(7, 3)
10.
What is the solution to this system of linear equations?
Use elimination.

       3x + y = -14
-2x - y = 9
a)
(-5, 1)
b)
(-1, -11)
c)
(5, -29)
d)
(13, 55)
11.
What is the value of y in the solution to this system of linear equations?      
Use elimination.

x + 3y = 18  
- x – 4y = - 25
a)
-7
b)
2
c)
6
d)
7
12.
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
13.
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
14.
Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?
a)
4x + 7y = 578
x + y = 3365
b)
4x + 7y = 3365
x + y = 578
c)
4y + 7x = 578
x + y = 3365
d)
4y + 7x = 3365
x + y = 578
Answer Key

Solving System of Equations Word Problems

Total questions: 14

1.
a) x + y = 21
6x + 4y = 104
2.
a) (10, 11)
3.
a) 1.5x + 0.5y = 78.5
x + y = 87
4.
a) (35, 52)
5.
c) 12 horses, 16 chickens
6.
c) (-3, 0)
7.
a) 0
8.
b) (-3, -6)
9.
d) (7, 3)
10.
a) (-5, 1)
11.
d) 7
12.
a) x + y = 6
14.80x + 17y = 91
13.
c) x + y = 49
20x + 50y = 1430
14.
b) 4x + 7y = 3365
x + y = 578

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FAQs

What does this systems of equations word-problems worksheet cover?

This Grade 9 worksheet uses 14 multiple-choice questions to practice translating real-world situations into systems of two linear equations and solving those systems. Students work with ticket sales, concession items, animals, restaurant orders, bills, and movie sales, using substitution or elimination to find an ordered pair or a requested value.

How can I use this worksheet to teach students to model systems from word problems?

Begin by having students label each variable and identify the two kinds of information in each scenario, such as total items and total cost. Model how a ticket, restaurant, or currency problem becomes one counting equation and one value equation, then ask students to explain why each coefficient and constant belongs in its equation before solving. Use the later substitution and elimination items to connect the model to an algebraic solution.

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

Students may put the total number of tickets, bills, or people in the cost equation, or put the total dollar amount in the counting equation. They may also reverse the variable assignments, swap prices such as adult and child tickets, mishandle decimal coefficients, or make sign errors while using substitution or elimination. Have students check whether their ordered pair satisfies both equations and matches the requested quantity.

How do I assign and grade this systems of equations worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. Assign the PDF for written practice or use the digital version for online responses; printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable option can also support schools that are reducing screen time.

How does this worksheet practice both substitution and elimination?

The worksheet includes separate multiple-choice items that explicitly ask students to solve systems using substitution and others that require elimination. Students must follow the appropriate algebraic method, then interpret whether the result should be an ordered pair or only the value of x or y. The word-problem items extend those methods by requiring students to solve systems after translating prices, quantities, and totals into equations.

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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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