# 3.12: Solving Linear Systems in Three Variables

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**Practice**Systems of Linear Equations in Three Variables

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Consistent

A system of equations is consistent if it has at least one solution.eliminating a variable

Eliminating the variable means making the coefficient of the variable equal to zero thereby removing that variable from that particular system and reducing the number of unknown quantities.Inconsistent

A system of equations is inconsistent if it has no solutions.linearly independent

Three equations are linearly independent if each equation cannot be produced by a linear combination of the other two. Systems that are linearly independent will have just one solution.scaling a row

Scaling a row means multiplying every coefficient in the row by any number you choose (besides zero). This can be helpful for getting coefficients to match so that they can be eliminated.system of equations

A system of equations is a set of two or more equations.### Image Attributions

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This lesson covers solving a system of equations in three variables (x, y, and z).

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Date Created:

Mar 12, 2013
Last Modified:

Jun 07, 2016
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