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Solving systems of equations underpins much of advanced algebra, especially linear algebra. Developing an intuition for the kinds and descriptions of solutions is key for success in those later courses. This intuition is exactly what this presentation aims to develop. Solving systems of linear equations through graphing is thoroughly demonstrated through careful vocabulary introduction and use, along with step-by-step examples. Integration of online graphing tools into the presentation and the editable format enable you to customize this for individual or class-wide viewing. A great introduction or refresher for one of the first methods of solving linear systems.

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##### Instructional Ideas

- Have each learner or group graph answers by hand, on a computer, and by calculator, then compare ease and accuracy of results
- Extend by giving coordinate points to the class and have them devise systems of equations with the given solution
- Give each pupil or group an equation of a line then ask them to find equations for consistent dependent, consistent independent, and inconsistent solutions

##### Classroom Considerations

- Presentation assumes that all given systems have only two equations. Systems with three or more equations require further explanation of possible solution arrangements
- Presentation is saved as a .pptx, which may present version compatibility issues
- Interactive solver in example problems requires Internet access

##### Pros

- Clear and complete explanation of types of systems and what the solutions look like and mean in context
- Examples of both consistent and inconsistent systems
- Completely worked example problems with links to interactive online graphing software pre-filled with class problem
- Keystroke directions for finding solutions to systems of equations on TI-83/84/Nspire calculators

##### Cons

- Fractions on slides 15 and 16 are missing the fraction bars
- No example 2 between examples 1 and 3

##### Common Core

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