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# Chapter 5

### Systems

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

What is the Addition Property of Inequality Multiplication Properties of Inequality? | For all real numbers a, b, and c: if a is less than b, than a+c is less than b+c. If a is less than b and c is greater than 0 then ac is less than bc. If a is less than b and c is less than 0, then ac is greater than bc. |

What is a consistent system? | A system which has one or more solutions is called a consistent system. |

What is an inconsistent system? | A system which has no solutions is called an inconsistent system. |

What is the intersection of two sets? | The intersection of two sets is the set consisting of those values common to both sets. |

What is the union of two sets? | The union of two sets is the set consisting of those values in either one or both sets. |

What is the solution set for a system? | The solution set for a system is the intersection of the solution sets for the individual sentences. When the system involves two equations each with two variables, the solution can often be found by making a table of values or a graph. |

What is a 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. |

What is a half-planes? | When a line is drawn in a plane, the line separates the plane into two distinct regions is called half-planes. The line itself is the boundary of the two regions. The boundary does not belong to either half plane. |

What is a feasible set or feasible region? | The set of solutions to a system of linear inequalities is often called feasible set or feasible region for that system. |

What is the 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. |

What steps should be followed to solve a linear-programming problem? | Follow these steps: 1. Identify the variables. 2. Identify the contraints, and translate them into a system of inequalities relating the variables. 3. Graph the system. 4.Write a formula or an expression.5.Apply the theorem. 6. Interpret the results. |

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Southlawn