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# 3.1-3.5 AlgebraIIHon

### Systems of equations and inequalities

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

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

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

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

Independent | A system of equations that is consistent and has one solution. |

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

Substitution Method | An algebraic method in which 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 | An algebraic method in which one of the variables is eliminated by adding or subtracting the equations. When the two true equations are added, the result is a new equation that is also true. |

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

Constraints | Inequalities |

Feasible Region | The intersection of the graphs. |

Bounded | When the graph of a system of constraints is a polygonal region. |

Vertices | Where the maximum or minimum value of a related function occurs at the feasible region. |

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

Ordered Triple | The solution of a system of equations in three variables x, y, and z and is written (x,y,z) |

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

Octants | Planes that intersect at right angles and divide space into eight regions. |

Ordered Triple | A point in space (three dimensions) that has three coordinates and is represented by (x,y,z). |

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