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One solution, No solution, infinitely many - Printable Mathematics Worksheets year 9 - Wayground

One solution, No solution, infinitely many

12 questions

9th - 9th Grade

Mathematics

One solution, No solution, infinitely many is a Grade 9 mathematics worksheet focused on classifying linear equations by their number of solutions. Students identify the first step in solving an equation, define one solution, no solution, and infinitely many solutions, and determine the solution type for equations with matching variable terms, constants, parentheses, and terms on both sides. The worksheet includes 11 multiple-choice questions and one multiple-select question. This free printable worksheet helps students connect algebraic simplification to the meaning of an equation: a single value can make it true, no value can make it true, or every value can make it true. It is useful for guided practice, independent review, or a quick formative check after teaching linear equations and solution types. A complete answer key is included for efficient checking and feedback.

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One solution, No solution, infinitely many

Total questions: 12

Name
Class
Date
1.
What is the first step to solve this equation:
11 - 3x = 44
a)
Add 3 to both sides
b)
Subtract 11 from both sides
c)
Add 11 to both sides
d)
Divide 3 on both sides.
2.
What is the solution to this equation?
a)
one solution
b)
no solution
c)
infinite solutions
d)
none of these
3.

What is the definition of one solution?

a)

no matter what constant is substituted in for the variable, the equation is ALWAYS true

b)

no matter what constant is substituted in for the variable, the equation will NEVER be true

c)

only this ONE solution will make the equation true

4.

What is the definition of infinite solutions?

a)

no matter what constant is substituted in for the variable, the equation is ALWAYS true

b)

no matter what constant is substituted in for the variable, the equation will NEVER be true

c)

only this ONE solution will make the equation true

5.

What is the definition of no solution?

a)

no matter what constant is substituted in for the variable, the equation is ALWAYS true

b)

no matter what constant is substituted in for the variable, the equation will NEVER be true

c)

only this ONE solution will make the equation true

6.

How many solutions does this equation have?


6x - 3 = 6x + 9

a)

One Solution

b)

No Solution

c)

Many Solutions

7.

How many solutions does this equation have?


8y - 4 = 8y - 4

a)

One Solution

b)

No Solution

c)

Infinitely Many Solutions

8.

How many solutions does this equation have?


2x + 9 = 2x + 9

a)

One Solution

b)

No Solution

c)

Infinitely Many Solutions

9.

How many solutions does this equation have?


3z + 7 = 7 + 3z

a)

One Solution

b)

No Solution

c)

Infinitely many solutions

10.

Which answer represents an equation with infinite solutions?

a)

2x = 2x

b)

5≠6

c)

3x = 7

d)

3=3

11.

How many solutions does the following equation have?

−2x + 9 + 6x = −3x + 2

a)

One Solution

b)

No Solutions

c)

Infinitely Many Solutions

d)

Two solutions

12.

How Many Solutions Does

This Equation Have?


7(2x + 5) = 12x – 1

a)

One Solution

b)

No Solution

c)

Infinitely Many Solutions

Answer Key

One solution, No solution, infinitely many

Total questions: 12

1.
b) Subtract 11 from both sides
2.
b) no solution
3.
c)

only this ONE solution will make the equation true

4.
a)

no matter what constant is substituted in for the variable, the equation is ALWAYS true

5.
b)

no matter what constant is substituted in for the variable, the equation will NEVER be true

6.
b)

No Solution

7.
c)

Infinitely Many Solutions

8.
c)

Infinitely Many Solutions

9.
c)

Infinitely many solutions

10.
d)

3=3

11.
a)

One Solution

12.
a)

One Solution

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FAQs

What does this worksheet cover, and how does it help students classify linear equations?

This Grade 9 worksheet practices identifying the first solving step and classifying linear equations as having one solution, no solution, or infinitely many solutions. Its 11 multiple-choice and one multiple-select item require students to connect simplified equations and definitions with the correct solution type, including equations with matching variable terms and equations that require combining terms or using the distributive property.

How can I use this worksheet to teach one solution, no solution, and infinitely many solutions?

Begin by modeling the first-step item, then show how simplifying both sides can reveal whether a variable has one possible value, produces a contradiction, or leaves an identity that is always true. Use the definition questions to establish the vocabulary before students classify the provided equations, and ask them to explain what the simplified variable and constant terms tell them. Finish with the multiple-select item as a check that students can recognize an equation representing infinitely many solutions.

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

Students may confuse “no solution” with “infinitely many solutions” by treating a contradiction and an identity as the same result. They may also cancel matching variable terms without checking the remaining constants, misread “only one solution” as “one side has one term,” or choose “many solutions” without recognizing that the worksheet’s category is infinitely many solutions. Check that students read the multiple-select directions carefully as well as the multiple-choice options.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can use the same one-solution, no-solution, and infinitely-many-solutions practice in either format. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable option can also support classrooms or schools 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 items and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language, while keeping the same solution-classification practice and question format.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across 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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