# 9.2 Systems of Equations in Three Variables

Solve systems of linear equations in three variables.

Use systems of three equations to solve applied problems.

Model a situation using a quadratic function.

A **linear equation in three variables** is an equation equivalent to one of the form $Ax+By+Cz=D$, where `A`, `B`, `C`, and `D` are real numbers and none of `A`, `B`, and `C` is 0. A **solution of a system of three equations in three variables** is an ordered triple that makes all three equations true. For example, the triple $(\mathrm{2,}\text{}-\mathrm{1,}\text{}0)$ is a solution of the system of equations

We can verify this by substituting 2 for `x`, $-1$ for `y`, and 0 for `z` in each equation.

# Solving Systems of Equations in Three Variables

We will solve systems ...

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