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# c h a p t e r 5

### Systems

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

compound sentence | A sentence in which two clauses are connected by the word and or by the word or |

union | the set consisting of those values in either one or both sets. |

Addition Property of Inequality | If a<b, then a+c < b+c |

Multiplication of Properties Inequality | If a < b and c > 0, then ac < bc. If a < b and c < 0, then ac > bc. |

Linear Combination Method | Involves adding multiples of the given equations. |

System-Determinant Theorem | A 2 X 2 system has exactly one solution if and only if the determinant of the coefficient matrix is NOT zero. |

which side is the equation x > 5 shaded | It is a dotted line shaded to the right |

Feasible Set | The set of solutions to a system of linear inequalities |

Vertices | It is the intersections of the boudaries (lines) |

Linear-Programming Theorem | The feasible region of every linear-programming problem is convex, and the maximum or minimum quantity is determined at one of the vertices of this feasible region. |

Steps to solve a linear-programming problem | 1. Identify variables 2. Identify the constraints 3. Graph system; find vertices of feasible set 4. Write a formula or an expression 5. Apply the Linear-Programming Theorem. 6. Interpret the results. |

Created by:
katelesperance