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Writing Systems of Equations Review

20 questions

11th - 11th Grade

Mathematics

Writing Systems of Equations Review is a Grade 11 mathematics worksheet with 20 multiple-choice questions that builds skill in translating real-world situations into equations and systems of equations. Students identify variables, match words to mathematical operations, and select equations that represent costs, quantities, totals, rates, and comparisons. Items include one-variable situations, such as change and ticket or meal costs, as well as systems involving ticket sales, product purchases, pricing plans, bills, and food quantities. This worksheet is designed for review, guided practice, or a formative check after instruction on writing linear equations and systems from context. The multiple-choice format helps teachers quickly identify whether students can distinguish a total from a unit cost, assign variables correctly, and preserve the relationships described in a situation. It is a free printable worksheet with an answer key, and it can support independent practice, partner discussion, or whole-class error analysis.

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Worksheets

Writing Systems of Equations Review

Total questions: 20

Name
Class
Date
1.
What equation matches this situation?
John wants to buy an MP3 Player that costs $30.98.  How much change did he receive if he gives the cashier $40.
a)
40 + c = 30.98
b)
30.98 + c = 40
c)
c - 40 = 30.98
d)
c - 30.98 = 40
2.
What do the following terms mean:
is
equal
the same as 
a)
+
b)
-
c)
=
d)
x
3.
Write an equation models the following statement:
 17 less than h equals 42
a)
17-h=42
b)
h-17=42
c)
h+17=42
d)
17+h=42
4.
4. There are 3 tennis balls in each can.  The coach bought a total of 27 tennis balls.  Which choice models this situation?
a)
x/3 = 27
b)
27x = 3
c)
x/27 = 3
d)
3x = 27
5.

Last Friday Stefan had $35. Over the weekend, his parents gave him some money for washing the car and now he has $47. Write an equation to determine how much his parents paid him for washing the car.

a)

35−x=4735-x=47

b)

x35=47\frac{x}{35}=47

c)

35+x=4735+x=47

d)

35x=4735x=47

6.

Mr Carrillo's family bought lunch from Culvers. They also bought some sodas from Quick Trip for $5.00. The meals cost $6.00 each. The total cost of the lunch and soda was $41.00. Let x represent the cost of the number of meals that Mr. Carrillo bought. Write the equation and solve for x.

a)

-5+6x = 41, 4 meals

b)

6x + 5 = 41, 6 meals

c)

6x = 36 meals

d)

5 + 6x = 41, 7 meals

7.
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)
a + c = 21
6a + 4c = 104
b)
a + c = 104
6a + 4c = 21
c)
a + c = 21
6c + 4a = 104
d)
a + c = 104
6c + 4a = 21
8.
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
9.
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used? 
a)
1s + 3c = 38
2s + 3c = 52
b)
3s + 1c = 38
3s + 2c = 52
c)
s + c = 38
s + c = 52
d)
3s + 3c = 38
1s + 2c = 52
10.
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
11.
On Monday Joe 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
12.
At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables? 
a)
t: # of tacos
m: # of glasses of milk
b)
t: Cost of each taco
m: Cost of each glass of milk
c)
t: total cost
m: # of food items
d)
t: Cost of each glass of milk
m: Cost of each taco
13.
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
14.
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
15.
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
16.

Match a sentence with this equation: C = 7.50p + 3.00C\ =\ 7.50p\ +\ 3.00  

a)

JB's Deli charges $ 0.75 for each pizza and $3.00 per topping

b)

Sally's Pizza  charges $3.00 per pizza with a $7.50 delivery fee

c)

Pizza Time charges $7.50 for each pizza and $.30 for the delivery fee

d)

Pizza Planet charges $7.50 per pizza with a $3.00 delivery fee

17.

Michael spent $50 for 6 tigerfish and 8 goldfish. Shaun spend $5 more than Michael for 5 tigerfish and 10 goldfish. Write a system of equations that could be use the find t, the price of a tigerfish and g, the price of a goldfish.

a)

8t+6g=508t+6g=50
10t+5g=5510t+5g=55

b)

6t+8g=506t+8g=50
5t+10g=455t+10g=45

c)

6t+8g=506t+8g=50
5t+10g=555t+10g=55

d)

8t+6g=508t+6g=50
10t+5g=4510t+5g=45

18.

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

19.

Tania had 35 coins in pennies and nickels. She had $1.03. Which system of equations could be used to determine the number of coins she has?

a)

.01p + .05n = 35

p + n = 103

b)

1p + 5n = 1.03

p + n = 35

c)

.01p + .05n = 1.03

p + n = 35

d)

.05p + .01n = 1.03

p + n = 35

20.
There are 15 animals in a barn.  These animals are horses and chickens.  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
Answer Key

Writing Systems of Equations Review

Total questions: 20

1.
b) 30.98 + c = 40
2.
c) =
3.
b) h-17=42
4.
d) 3x = 27
5.
c)

35+x=4735+x=47

6.
b)

6x + 5 = 41, 6 meals

7.
a) a + c = 21
6a + 4c = 104
8.
c) 4x+3y=134
3x+3y=120
9.
b) 3s + 1c = 38
3s + 2c = 52
10.
a) x + y = 1550
y  = 4x
11.
b) 10c + 5d = 16.50
5c + 10d = 14.25
12.
b) t: Cost of each taco
m: Cost of each glass of milk
13.
b) y = 9.65x + 43
y = 8.40x + 58
14.
c) x + y = 49
20x + 50y = 1430
15.
b) 5q + 2z = 1.32
3q + 1z = 0.75
16.
d)

Pizza Planet charges $7.50 per pizza with a $3.00 delivery fee

17.
c)

6t+8g=506t+8g=50
5t+10g=555t+10g=55

18.
a)

S + A = 530

3S + 4A = 1740

19.
c)

.01p + .05n = 1.03

p + n = 35

20.
a) x + y = 15
4x + 2y = 44

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FAQs

What does the Writing Systems of Equations Review worksheet cover?

This Grade 11 worksheet uses 20 multiple-choice questions to practice translating verbal situations into linear equations and systems of equations. Students identify variables and select models for problems involving change, quantities, ticket totals, combined costs, unit prices, and relationships such as one amount being four times another.

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

Begin by having students underline quantities, totals, and relationships in each word problem, then define what each variable represents before choosing an equation. Use the ticket, brochure, meal, and bill scenarios to discuss why each condition becomes a separate equation and ask students to explain why the coefficients match the quantities described.

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

Watch for reversed relationships, such as writing 17 − h instead of h − 17 for “17 less than h,” and for confusing a total number of items with a total dollar amount. Students may also omit a second equation in a system, swap variable meanings, or use the wrong coefficient when translating quantities such as 3 senior tickets or 20-dollar bills.

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

The worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for all 20 multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app, while the digital quiz supports online completion and grading.

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-problem choices are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language, depending on students’ needs.

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

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