Number of Solutions in Systems of Equations

Grade 11 Math worksheet focusing on determining the number of solutions (one, none, or infinitely many) for linear and non-linear systems of equations.

Grade 11 Math AlgebraNumber of Solutions

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Includes

2 Multiple Choice2 Short AnswerFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSA.REI.C.6CCSS.MATH.CONTENT.HSA.REI.C.7CCSS.MATH.CONTENT.HSA.REI.D.11

Topics

AlgebraSystems of EquationsNumber of SolutionsGrade 11

8 sections · Free to use · Printable

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Number of Solutions in Systems of Equations

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Read each question carefully and determine the number of solutions for each system of equations. Choose the best answer or write your explanation where prompted.

1. How many solutions does the following system of equations have? y = 3x - 5 6x - 2y = 10

One solution

No solution

Infinitely many solutions

Cannot be determined

2. Consider the system of equations: y = -x + 4 y = 2x + 1 Graph the two lines on the coordinate plane below and determine the number of solutions.

Number of Solutions:

3. If two linear equations in a system have the same slope but different y-intercepts, the system has solutions. This indicates the lines are .

4. If two linear equations in a system have different slopes, they will intersect at exactly point, meaning there is solution.

5. A system consisting of a circle and a line can have a maximum of how many solutions?

One

Two

Three

Infinitely many

6. A system of two distinct parabolas can have at most four solutions.

True

False

7. Determine the number of solutions for the system: y = x^2 - 4x + 3 y = -x + 3 Explain your reasoning. (Hint: Use substitution or elimination.)