MA.912.A.3.14Archived Standard

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Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods.

Remarks

Example 1: Solve the following system of equations by substitution:


Example 2: Graph the solution for the following system of inequalities:



Example 3: Solve the following system of equations:

General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Standard: Linear Equations and Inequalities - Solve linear equations and inequalities.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , FR item(s)
    • Also Assesses:

    MA.912.A.3.13 Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology.

    MA.912.A.3.15 Solve real-world problems involving systems of linear equations and inequalities in two and three variables.
  • Clarification :
    Students will solve systems of linear equations in two variables.
  • Content Limits :

    Items will not specify a method for solving systems of linear equations, such as substitution or elimination.

    Items will not assess systems of linear inequalities.

    Items will not assess systems of linear equations in three variables.

    Items may ask students to write and/or solve systems of linear equations in two variables.

    Items may ask students to solve systems of linear equations given a graph of the system.

    In items with equations given, equations may be in the stem or options.

  • Response Attributes :
    Fill-in response items may ask students to provide the x-coordinate (or y-coordinate) of a solution to a system of linear equations.
Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question: Russ bought 3 medium and 2 large submarine sandwiches for a total of $29.95. Stacy bought 4 medium and 1 large submarine sandwiches for a total of $28.45.
    Which statement shows the cost of each medium and each large submarine sandwich?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question:

    A website that sells songs for downloading increased its price per song from $0.99 to $1.29. Macy spent $15.36 downloading songs during the month of the price increase. She downloaded 4 more songs at $0.99 than at $1.29. The set of equations below represents the situation where x is the number of songs Macy downloaded at $0.99 and y is the number of songs she downloaded at $1.29.

    x = y + 4
    0.99x + 1.29y = 15.36

    What is the exact number of songs Macy downloaded at the $0.99 price?

  • Difficulty: N/A
  • Type: FR: Fill-in Response

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Video/Audio/Animation

Solving Systems by Substitution 1: No Solution:

This video demonstrates the substitution method to solve a system of equations, that there is no solution, and that the graphs of the equations are parallel.

Type: Video/Audio/Animation

Student Resources

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Parent Resources

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