Infinitely Many Solutions

This worksheet focuses on identifying and solving systems of linear equations with infinitely many solutions at a Grade 12 level, including algebraic and graphical interpretations.

Grade 12 Math AlgebraSystems of EquationsInfinitely Many Solutions

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Multiple ChoiceFill in the BlanksShort AnswerCustomTrue / FalseLong Answer

Standards

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

8 sections · Free to use · Printable

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Infinitely Many Solutions

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Read each question carefully and provide the best answer. Show all your work for full credit. For systems of equations, clearly state whether there is one solution, no solution, or infinitely many solutions.

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

2x + 3y = 6 4x + 6y = 10

x - y = 5 2x - 2y = 10

3x + y = 7 3x - y = 7

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

2. A system of linear equations has infinitely many solutions when the graphs of the equations are .

3. When solving a system of equations algebraically, if you arrive at a true statement (e.g., 0 = 0), it indicates that the system has solutions.

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

Equation 1: 3x - 2y = 12

Equation 2: 6x - 4y = 24

5. Graph the following system of equations and describe the solution set:

y = -x + 3

2y = -2x + 6

Description of solution set:

6. If two lines in a system of equations have the same slope and different y-intercepts, the system has infinitely many solutions.

True

False

7. Consider the system of equations:

Equation 1: Ax + 4y = 8

Equation 2: 3x + By = 12

Find the values of A and B that would result in the system having infinitely many solutions. Show your work and justify your answer.