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System of Equations WordProblems - Printable Mathematics Worksheets - Wayground

System of Equations WordProblems

14 questions

9th - 9th Grade

Mathematics

System of Equations WordProblems is a Grade 9 mathematics worksheet with 14 multiple-choice questions focused on interpreting and modeling systems of linear equations. Students identify whether graphs show parallel, intersecting, or coincident lines; determine the number of solutions; choose a correct substitution setup; and translate situations involving prices, quantities, ages, bills, recipes, and sales into systems of equations. The worksheet also asks students to connect a modeled system with its solution, including ordered pairs and values such as unit costs or quantities. These items help teachers check whether students can distinguish total-quantity equations from value equations, assign variables consistently, and preserve the relationships described in a word problem. This free printable worksheet is designed for Grade 9 math practice, review, or assessment and includes a complete answer key.

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Worksheets

System of Equations WordProblems

Total questions: 14

Name
Class
Date
1.
If a system of equations has no solution, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
2.
How many solutions does this system of equations have?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
d)
Two Solutions
3.
If a system of linear equations has one solution, what does this mean about the two lines? 
a)
Parallel lines
b)
the same line 
c)
Intersecting lines
4.
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.  Which system of equations represents the situation?
a)
3x + 2y = 315
2x + 4y = 450
b)
3x + 2y = 450
2x + 4y = 315
c)
2x + 2y = 315
3x + 4y = 450
5.

What is the proper way to set up the equation to begin solving?


y = 6x − 11

−2x − 3y = −7

a)

-2(-11) -3y= -7

b)

-2(6x-11) -3y = -7

c)

-2x -3(11) = -7

d)

-2x - 3(6x-11)= -7

6.

Robert is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents this situation?

a)

x - y = -10 and x + y = -2

b)

x = -2 and y = -10

c)

x + y = -10 and x - y = -2

d)

x + y = -2 and x - y = -10

7.

Ruby won a bag full of money!! She has 49 bills in all. She counts a total of $1430 in the bag. There are twenty dollar bills and fifty dollar bills only. Which system best represents this situation?

a)

x + y = 1430 and 10x + 39y = 49

b)

x + y = 49 and 20x + 50y = 1430

c)

x + y = 49 and 10x + 39y = 1430

d)

x + y = 1430 and 20x + 50y = 49

8.

Makayla and KaReyniti visited a candy shop. Makayla bought 10 pounds of strawberry taffy and 1 pound of banana taffy for $46. KaReyniti bought 1 pound of strawberry taffy and 1 pound of banana taffy for $10. How much does each type of taffy cost?

a)

Strawberry cost $10 and Banana cost $36 per pound

b)

Strawberry cost $3 and Banana cost $7 per pound

c)

Strawberry cost $7 and Banana cost $3 per pound

d)

Strawberry cost $4 and Banana cost $6 per pound

9.

Yesterday a chef used 68 eggs to make 8 chocolate souffles and 10 lemon meringue pies. The day before, he made 7 chocolate souffles and 10 lemon meringue pies, which used 62 eggs. How many eggs, does each dessert require? If (x) represents chocolate souffles and (y) represents lemon meringue pies, give the correct system of equations and the solution as an ordered pair.

a)

8x + 10y = 68

7x + 10y = 62

( 2, 6 )

b)

8x + 10y = 68

7x + 10y = 62

( 6, 2 )

c)

7x + 10y = 68

8x + 10y = 62

( 5, 4 )

d)

7x + 10y = 68

8x + 10y = 62

( 5, 3 )

10.

Bob bought a total of 20 pounds of grass seed at the nursery for $128. He paid $9 per pound of Kentucky bluegrass (k) and $6 per pound for Tall Fescue (f). Which system of equations can be used to find the amount of each that Bob purchased?

a)

k + f = 168

9k + 6f = 20

b)

k + f = 168

6k + 9f = 20

c)

k + f = 20

9k + 6f = 128

d)

k + f = 20

6k + 9f = 128

11.
Mofor and Matt are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Mofor sold 11 rolls of plain wrapping paper and 7 rolls of shiny wrapping paper for a total of $79. Matt sold 5 rolls of plain wrapping paper and 7 rolls of shiny wrapping paper for a total of $55. What is the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper?
a)
plain $4 and shinny $6
b)
plain $6 and shinny $4
c)
plain $4 and shinny $5
d)
plain $5 and shinny $4
12.
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
13.
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
14.
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
Answer Key

System of Equations WordProblems

Total questions: 14

1.
b) parallel lines
2.
c) Infinitely Many Solutions
3.
c) Intersecting lines
4.
a) 3x + 2y = 315
2x + 4y = 450
5.
d)

-2x - 3(6x-11)= -7

6.
c)

x + y = -10 and x - y = -2

7.
b)

x + y = 49 and 20x + 50y = 1430

8.
d)

Strawberry cost $4 and Banana cost $6 per pound

9.
b)

8x + 10y = 68

7x + 10y = 62

( 6, 2 )

10.
c)

k + f = 20

9k + 6f = 128

11.
c) plain $4 and shinny $5
12.
b) x + y = 33
x = 2y - 3
13.
c) 4x+3y=134
3x+3y=120
14.
a) 1.5x+0.5y=78.5
x+y=87

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FAQs

What does this systems of equations worksheet cover?

This Grade 9 worksheet uses 14 multiple-choice questions to practice identifying graph relationships and translating word problems into systems of linear equations. Students model situations involving prices, quantities, ages, bills, recipes, and sales, then connect selected systems to solutions such as ordered pairs or unit costs.

How can I use this worksheet to teach translating word problems into systems of equations?

Have students define each variable and underline the two quantities or totals described in each scenario before choosing an equation pair. Use the haircut, taffy, and concession-stand questions to discuss how one equation represents a count or combined amount while the other represents a cost or time total. Then ask students to check whether a selected system matches both details in the original situation.

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

Students may reverse the variable meanings, confuse a total number of items with a total cost, or place the wrong coefficient beside a variable. Watch for errors such as writing 20x + 50y = 49 instead of matching the 49 bills and $1,430 total, or reversing Alex and Erin's age relationship. In the graph and substitution items, students may also confuse parallel lines with intersecting lines or substitute into only part of an expression.

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, and it includes a complete answer key for all 14 multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time.

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

Because the worksheet contains text-heavy multiple-choice word problems, you can adjust font spacing and font size to make the scenarios and answer choices easier to scan. Wayground’s Advanced Settings also allow you to apply a dyslexia-friendly font or translate the worksheet into another language. These changes can support access to the modeling and equation-selection tasks without changing the questions.

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

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