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Infinitely Many Solutions in Systems of Equations

Explore systems of linear equations with infinitely many solutions, including identification and interpretation.

Grade 9 Math AlgebraSystems of EquationsInfinitely Many Solutions
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Includes

TextMultiple ChoiceFill in the BlanksShort AnswerCustomTrue / FalseMatching

Standards

CCSS.MATH.CONTENT.HSA-REI.C.5CCSS.MATH.CONTENT.HSA-REI.C.6

Topics

AlgebraSystems of EquationsInfinitely Many SolutionsGrade 9 Math
9 sections · Free to use · Printable
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Infinitely Many Solutions in Systems of Equations

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

A system of linear equations is said to have infinitely many solutions if the equations are dependent, meaning they represent the same line. When graphed, these lines perfectly overlap.

1. Which of the following systems of equations has infinitely many solutions?

a

2x + y = 5 x + y = 3

b

3x - 2y = 6 6x - 4y = 12

c

x + 2y = 4 x + 2y = 6

d

4x + y = 7 2x - y = 1

2. When a system of equations has infinitely many solutions, the lines are  .

3. To have infinitely many solutions, the equations in a system must be   of each other.

4. Explain how you can algebraically determine if a system of two linear equations has infinitely many solutions.

5. Graph the system of equations below. What does the graph tell you about the number of solutions?

Equation 1: y = 2x - 3

Equation 2: 4x - 2y = 6

-10-8-6-4-2246810-10-8-6-4-2246810

6. If you multiply one equation in a system by a constant and get the other equation, the system has infinitely many solutions.

T

True

F

False

7. Match the system of equations with its description.

A. x + y = 5 2x + 2y = 10

 

i. No solution

B. y = 3x - 1 y = 3x + 2

 

ii. Infinitely many solutions

C. x + y = 4 x - y = 2

 

iii. One solution

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