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Writing Systems of Equations - Printable Mathematics Worksheets - Wayground

Writing Systems of Equations

10 questions

9th - 9th Grade

Mathematics

Writing Systems of Equations is a Grade 9 mathematics worksheet that helps students translate real-world situations into systems of two linear equations. Through 10 multiple-choice questions, students identify equations for scenarios involving bills, food purchases, tickets, produce, brochures, service times, coins, plates, and restaurant costs. Each item requires students to connect quantities, prices, measurements, or totals to the correct algebraic representation. This free printable worksheet with an answer key is useful for introducing or reviewing how to define variables, write a total-quantity equation, and write a total-value or cost equation. Students must distinguish between the number of objects and their combined value, match coefficients to the quantities described, and place dollar or measurement totals correctly. Use it as guided practice, independent classwork, homework, or a formative check before students solve systems of equations.

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Worksheets

Writing Systems of Equations

Total questions: 10

Name
Class
Date
1.

Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. 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

2.

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

3.
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

4.

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations that represents this situation. Let q represent the number of squash purchased and let z represent the number of zucchini purchased.

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
5.
Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?
a)
x+y=134
x+y=120
b)
3x+3y=134
4x+3y=120
c)
4x+3y=134
3x+3y=120
d)
7xy=134
6xy=120
6.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Let h represent the number of haircuts given and d represent the number of hair dyes done. Which system of equations represents the situation?

a)

3h + 2d = 315

2h + 4d = 450

b)

3h + 2d = 450

2h + 4d = 315

c)

2h + 4d = 315

3h + 2d = 450

d)

3h + 2d = 315

2h + 2d = 135

7.

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. 


Which systems of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?

a)

0.10q+0.25d=2.850.10q+0.25d=2.85  
q+d=18q+d=18  

b)

0.10q+0.25d=180.10q+0.25d=18  
q+d=2.85q+d=2.85  

c)

0.25q+0.10d=2.850.25q+0.10d=2.85  
q+d=18q+d=18  

d)

0.25q+0.10d=180.25q+0.10d=18  
q+d=2.85q+d=2.85  

8.

There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 15 plates combined is 140 inches.

Which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?

a)

x+y=140x+y=140  
12x+7y=1512x+7y=15  

b)

7x+12y=1407x+12y=140  
7x+12y=157x+12y=15  

c)

x+y=15x+y=15  
7x+12y=1407x+12y=140  

d)

x+y=15x+y=15  
12x+7y=14012x+7y=140  

9.
You have a total of 17 coins.  All of your coins are nickels and dimes.  The total value of the coins is $1.35.  Which system of equations represents this situation?
a)
n+d=17
.05n+.10d=1.35
b)
.05n+.10d=17
n+d=1.35
c)
.25n+.10d=1.35
n+d=17
10.

At a restaurant, the cost for 2 burritos and 1 tortilla salad is $20.57. The cost for 3 burritos and 3 tortilla salads is $36.24. Which pair of equations can be used to determine b, the cost of a burrito, and t, the cost of a tortilla salad?

a)

b + t = 20.57


3b + 3t = 36.24

b)

2b + t = 20.57


3b + 3t = 36.24

c)

2b + t = 20.57


b + t = 36.24

d)

b + 2t = 20.57


b + t = 36.24

Answer Key

Writing Systems of Equations

Total questions: 10

1.
c)

x + y = 49

20x + 50y = 1430

2.
c)

4x + 6y = 13

3x + 7y = 13.5

3.
a)

s + a = 530

3s + 4a = 1740

4.
b) 5q + 2z = 1.32
3q + 1z = 0.75
5.
c) 4x+3y=134
3x+3y=120
6.
a)

3h + 2d = 315

2h + 4d = 450

7.
c)

0.25q+0.10d=2.850.25q+0.10d=2.85  
q+d=18q+d=18  

8.
c)

x+y=15x+y=15  
7x+12y=1407x+12y=140  

9.
a) n+d=17
.05n+.10d=1.35
10.
b)

2b + t = 20.57


3b + 3t = 36.24

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FAQs

What does the Writing Systems of Equations worksheet help students practice?

This Grade 9 worksheet helps students write systems of two linear equations from word problems rather than solve the systems. Its 10 multiple-choice items require students to translate quantities and totals—such as bills, tickets, coins, food items, plate diameters, and service times—into equations with correctly matched variables, coefficients, and constants.

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

Begin by modeling one item: have students define the variables, identify the total-number relationship, and then identify the total-cost, value, time, or measurement relationship. For example, in the ticket problem, students can explain why the number of student and adult tickets forms one equation while their $3 and $4 prices form the second. Then use the remaining multiple-choice items for partner reasoning, asking students to eliminate choices with swapped totals, coefficients, or variables before selecting an answer.

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

Students may write the total money or measurement as the number of items, such as using a ticket total as the sum of prices, or they may reverse the two equations. Watch for coefficients that do not match the quantities in the story, variables assigned to the wrong item, and decimal values placed with the wrong coin or product. The multiple-choice distractors are especially useful for identifying these translation errors.

How do I assign and grade this Writing Systems of Equations worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for all 10 multiple-choice questions. Teachers can grade printable submissions by scanning student work with the Wayground for Teachers app. The printable format also supports classrooms that are reducing screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equation choices and word-problem details are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language, while keeping the 10 multiple-choice system-writing tasks intact.

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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