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# Equations

### MTH005 Ch 2 Special Cases

Special Case | Description |
---|---|

Conditional equation graphing solution set | If the variable has no exponent, the graphs of the left & right sides of the equation intersect at one point (x, y); x is the estimated solution of the equation. |

Contradiction equation solutin set | Empty set |

Identity equation solution set | All Real numbers |

Conditional equation definition | True or false depending on the replacement for the variable |

Contradiction equation definition | False for all replacements of the variable |

Identity equation definition | True for all replacements of the variable |

Conditional equation graph | Graphs of the left & right sides of the equation intersect at one point |

Contradiction eqution graph | Graphs of the left & right sides of the equation appear to be parallel lines (parallel lines never intersect; therefore there is no solution) |

Identity equation graph | Graphs of the left & right sides of the equation coincide (lines that coincide share all points in common; therefore all real numbers are solutions) |

Algebraic solution of a Conditional equation | Variable equals a number, if the variable has no exponent |

Algebraic solution a Contradiction equation | The variable is eliminated when solving, & the resulting equation is false (number = different number) |

Algebraic solution of an Identity equation | The variable is eliminated when solving, & the resulting equation is true (number = same number). |

TI-83+ or 84+ table for a Conditional eqation | If the variable has no exponent, there is only one value of x where Y1 and Y2 (values of the expressions) are equal (the same) |

TI-83+ or 84+ table for a Contradiction equation | Y1 and Y2 (values of the expressions) differ by the same amount for all values of the variable (x) |

TI-83+ or 84+ table for an Identity equation | Y1 and Y2 (values of the expressions) are the same for all values of the variable (x) |

Meaning of x and y (x, y) | x is the value of the variable when the equation is solved. y is the value of the expressions when the value of x is substituted for the variable and the resulting numeric expressions (left & right sides of the equation)are evaluated |

Created by:
powens