This Grade 9 mathematics worksheet gives students 12 multiple-choice questions on solving systems of linear equations in real-world contexts. Students translate restaurant bills, produce purchases, age relationships, concession sales, ticket prices, and transportation data into systems of equations, then identify or solve the resulting systems. Additional questions ask students to interpret ordered-pair solutions, use graphing to find an intersection, and classify systems as having one, no, or infinitely many solutions.
As a free printable worksheet with a complete answer key, it supports independent practice, guided review, homework, or a quick formative assessment. The varied word problems require students to connect verbal relationships with equations, while the graphing and solution-count items reinforce what a system’s solution means mathematically. It is designed for Grade 9 learners building fluency with modeling and solving systems of linear equations.
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Solving System of Linear Equation Word Problems
Total questions: 12
Name
Class
Date
1.
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
2.
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
3.
Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.
a)
x + y = 33 y = 2x - 3
b)
x + y = 33 x = 2y - 3
c)
x + y = 33 x = 3 - 2y
d)
x + y = 3 x = 33 - 2y
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.
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
6.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
7.
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
8.
How many solutions will this system have?
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
9.
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
10.
Solve the following system by graphing. What is the solution?
a)
Infinite number of solutions
b)
(3, 3)
c)
(3, -3)
d)
(-3, 3)
11.
How many solutions will this system have?
a)
No Solution
b)
Infinitely Many Solutions
c)
No Clue
d)
One solution
12.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
Answer Key
Solving System of Linear Equation Word Problems
Total questions: 12
1.
a)
x + y = 6 14.80x + 17y = 91
2.
b)
5q + 2z = 1.32 3q + 1z = 0.75
3.
b)
x + y = 33 x = 2y - 3
4.
a)
(35, 52)
5.
d)
Adult $12 Child $13
6.
d)
(1, 3)
7.
c)
Van 14 Bus 43
8.
a)
No solution
9.
c)
Intersect
10.
b)
(3, 3)
11.
b)
Infinitely Many Solutions
12.
d)
(1, 3)
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FAQs
What does this systems of linear equation word problems worksheet cover?
This Grade 9 worksheet contains 12 multiple-choice questions that ask students to model situations such as family restaurant bills, ticket sales, ages, and school transportation with systems of linear equations. It also checks whether students can solve systems, interpret ordered pairs, identify graph intersections, and determine whether a system has one, no, or infinitely many solutions.
How can I use this worksheet to teach students to model systems of linear equations?
Introduce the word problems by having students name the quantities represented by each variable before choosing an equation system. For each multiple-choice item, ask students to identify the total-number relationship and the total-cost or total-value relationship, then explain why the selected equations match the wording. Follow the modeling questions with the solution, graphing, and number-of-solutions items so students connect equations to ordered pairs and intersections.
What mistakes should I watch for when students complete this worksheet?
Students may assign variables inconsistently, reverse the relationship in the age problem, or confuse a total number of items or people with a total cost. In the ticket, produce, restaurant, and concession problems, check that coefficients represent quantities and prices are paired with the correct variables. Students may also mistake an ordered pair for two separate answers or confuse intersecting lines with systems that have no or infinitely many solutions.
How do I assign and grade this systems of linear equation word problems worksheet?
This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 12 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.
How can I differentiate this worksheet for my students?
Use the worksheet’s Advanced Settings to adjust font spacing and font size so the multi-step word problems and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language, helping students access the system-modeling and graphing questions in a more usable 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, 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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