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The Constructing consistent and inconsistent systems exercise appears under the 8th grade (U.S.) Math Mission and Algebra I Math Mission. This exercise helps to understand the properties that make lines consistent and inconsistent.

Types of Problems

There are two types of problems in this exercise:

  1. Find the coefficients to make a particular system: This problems provides the coefficients for one line and blanks for the coefficients on the other line. The student is asked to fill in those blanks correctly to produce a type of system.
    Ccais1

    Find the coefficients to make a particular system

  2. Select the correct value for a variable: This problem provides a system and one coefficient is replaced with a variable. The student is asked to determine what conditions on the variable will create a particular system of equations.
    Ccais2

    Select the correct value for a variable

Strategies

To complete this exercise knowledge of the algebraic properties of consistent and inconsistent systems are sufficient.

  1. In both inconsistent and dependent solutions, the slopes of the line must be equal, so multiplying a coefficient by a constant will cause the same multiplication against both the coefficients. The isolated number, will be lined up with this multiple if it dependent, and different if it is inconsistent.
  2. In the Select the correct value for a variable" problem, when making inconsistent systems, the answer will be "anything but n."

Real-life applications

  1. Systems of equations that are inconsistent mean the problem they model has no possible solution.
  2. Systems of equations that are dependent means there is not enough information to determine unique solutions.

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