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:
- 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.
- 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.
Strategies
To complete this exercise knowledge of the algebraic properties of consistent and inconsistent systems are sufficient.
- 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.
- In the Select the correct value for a variable" problem, when making inconsistent systems, the answer will be "anything but n."
Real-life applications
- Systems of equations that are inconsistent mean the problem they model has no possible solution.
- Systems of equations that are dependent means there is not enough information to determine unique solutions.