# Independent and Dependent Systems

##### This Independent and Dependent Systems presentation also includes:

Learners practice their linear algebra skills with laser focus on the unique cases of independent and dependent systems in this short problem set and presentation. The pairing of the two concepts really brings into focus the difference between a system having no solutions and having an infinite number of solutions, a hard distinction for many. Non-intimidating numerical values and clean calculations allow the emphasis of the lesson to rest on the recognition and interpretation of results, not the mechanics of the matrix reduction process.

##### Instructional Ideas

• Consider using as an activity in the flipped classroom model, assigning readings and videos about independent / dependent systems ahead of time
• Problems would make great bell-ringers or review problems after the concept is taught, particularly when mixed with problems with single solutions
• Try incorporating group work where the groups (or pairs) work so that each learner works a step of the elimination, then passes to the next person for checking and continuation
##### Classroom Considerations

• Main resource presentation is paired with the additional resource attachment of a student worksheet
• Presentation lends itself well to an interactive whiteboard adaptation, where each step is amended and revealed as the class works through the problems
• Last two problems on the student worksheet are not solved in the given presentation, could perhaps be done as seatwork after examples
##### Pros

• Clear and concise examples provided at the top of the student worksheet
• Problem set is short enough to avoid fatigue, while still covering the key characteristics of the system
##### Cons

• Second included resource is for a different lesson, converting between rectangular and polar coordinates, not solving systems using matrices
• Answers provided do not cover all of the student problems