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Thinking about solutions to systems
You know how to solve systems of equations (for the most part). This tutorial will take things a bit deeper by exploring cases when you might have no solutions or an infinite number of them.
Systems of equations without a solution
Consistent, but dependent systems of equations
Consistent and Inconsistent Systems
Independent and Dependent Systems
Going through a few examples on the Khan Academy practice exercise: http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/e/solutions_to_systems_of_equations
Determine how many solutions exist to a given system of equations (one, zero, infinite).
Use graphs to understand that substitution and elimination always produce equations consistent with the solution of the original system.