Systems of Equations: Infinitely Many Solutions

This worksheet focuses on identifying and solving systems of linear equations that have infinitely many solutions, a key concept in Grade 11 Algebra.

Grade 11 Math AlgebraSystems of EquationsInfinitely Many Solutions

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Includes

Multiple ChoiceFill in the Blanks2 Short AnswerGraphTrue / False

Standards

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

Topics

AlgebraSystems of EquationsInfinitely Many SolutionsGrade 11

8 sections · Free to use · Printable

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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.

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

2x + y = 5 4x + 2y = 8

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

x + y = 3 x - y = 1

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

2. A system of linear equations has infinitely many solutions if the equations represent the .

3. When solving a system of equations algebraically, if you arrive at an identity such as 0 = 0, the system has solutions.

4. Determine if the following system has infinitely many solutions. Explain your reasoning.

Equation 1: y = 3x - 2

Equation 2: 6x - 2y = 4

5. Graph the following system of equations on the coordinate plane below. What does the graph indicate about the number of solutions?

Equation 1: x + y = 3

Equation 2: 2x + 2y = 6

6. If two linear equations in a system are multiples of each other, then the system has infinitely many solutions.

True

False

7. For what value of 'k' will the following system of equations have infinitely many solutions?

Equation 1: 3x - 5y = 10

Equation 2: 9x - 15y = k