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Published byBridget Glenn Modified over 9 years ago

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Systems of Equations Summary

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Independent The equations of a linear system are independent if none of the equations can be derived algebraically from the others.

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Independence When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.

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Is this set of equations independent or dependent?

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Give a geometrical explanation of this system of liner equations.

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The three planes intersect on a line. There are an infinite number of solutions

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Consistent A linear system is consistent if it has a solution, and inconsistent otherwise. When the system is inconsistent, it is possible to derive a contradiction from the equations, that may always be rewritten such as the statement 0 = 1.

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Write a system of equations that describe 3 parallel planes. Is the system dependent or independent? Is the system consistent or inconsistent?

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Example Independent and inconsistent

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Write a system of equations that describe 2 parallel planes cut by a third plane. Is the system dependent or independent? Is the system consistent or inconsistent?

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Example Independent and inconsistent

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Write a system of equations that describe 3 planes that form a triangular prism. Is the system dependent or independent? Is the system consistent or inconsistent?

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Example Independent and inconsistent

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Write a system of equations that describe 3 planes that intersect on a line. Is the system dependent or independent? Is the system consistent or inconsistent?

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Example Dependent and consistent with an infinite number of solutions

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