Equation | x_{1} | x_{2} |
x_{3} | x_{4} | x_{5} |

(1) | 1 | 1 | 1 | ||

(2) | 1 | 1 | |||

(3) | 1 | 1 | 1 | ||

(4) | 1 | 1 | |||

(5) | 1 |

Rearranging and reordering the incidence table leaves us with:

Equation | x_{5} | x_{1} | x_{3} | x_{4} | x_{2} |

(5) | 1 | ||||

(4) | 1 | 1 | |||

(3) | 1 | 1 | |||

(1) | 1 | 1 | 1 | ||

(2) | 1 | 1 |

**2.**
The incidence table for the equation set is:

Equation | x_{1} | x_{2} |
x_{3} | x_{4} |

(1) | 1 | 1 | 1 | 1 |

(2) | 1 | 1 | 1 | 1 |

(3) | 1 | 1 | ||

(4) | 1 | 1 |

Rearranging and reordering the incidence table leaves us with:

Equation | x_{4} | x_{3} |
x_{1} | x_{2} |

(4) | 1 | 1 | ||

(3) | 1 | 1 | ||

(1) | 1 | 1 | 1 | 1 |

(2) | 1 | 1 | 1 | 1 |

In this case there is no head or tail. Instead all of the equations
form the partitions. Either of x_{2}, x_{3} or
x_{4} would be suitable for the tear variable here. x_{1}
would not be suitable as estimating a value for x_{1}
does not leave an equation with only one further unknown present.

**3.**
The incidence table for the equation set is:

Equation | x_{1} | x_{2} |
x_{3} | x_{4} |

(1) | 1 | 1 | ||

(2) | 1 | 1 | 1 | |

(3) | 1 | 1 | 1 | 1 |

(4) | 1 | 1 |

Rearranging and reordering the incidence table leaves us with:

Equation | x_{1} | x_{2} |
x_{3} | x_{4} |

(4) | 1 | 1 | ||

(1) | 1 | 1 | ||

(2) | 1 | 1 | 1 | |

(3) | 1 | 1 | 1 | 1 |

Equations (4), (1) and (2) form the partition here. This leaves
equation (3) to be the tail. There is no head. Either of x_{1},
x_{2} or x_{3} would be suitable choices for the tear
variable.

Return to Section 3.5.3: Non-linear Equations Questions