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# Linear Systems Vocab

### Section 3.1-3.5

Question | Answer |
---|---|

System of Equations | Two or more equations with the same variables. |

Consistent Solution | A system of equations that has at least one solution. |

Inconsistent Solution | A system of equations has no solution. |

Independent | A consistent system is independent if it has exactly one solution |

Dependent | A consistent system that has an infinite number of solutions. |

Substitution Method | An algebraic method where one equation is solved for one variable in terms of the other. Then, this expression is substituted for the variable in the other equation. |

Elimination Method | Another algebraic method, where you eliminate one of the variables by adding or subtracting the equations. When you add two true equations, the result is a new equation that is also true. |

System of Inequalities | A set of inequalities with the same variables. |

Constraints | Conditions given to variables, often expressed as linear inequalities. |

Feasible Region | The intersection of the graphs in a system of constraints. |

Bounded | A region is bounded when the graph of system of constraints is a polygonal region. |

Verticies | The maximum or minimum value that a linear function has for the points in a feasible region. |

Unbounded | A system of inequalities that forms a region that is open. |

Linear Programming | The process of finding the maximum or minimum values of a function for a region defined by inequalities. |

Ordered Triple | The coordinates of a point in space The solution of a system of equations in three variables x,y,and z |

Octants | The eight regions of three-dimensional space. |

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