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# Systems Solutions

### Types of Solutions for Systems of Equations

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

How many solutions does a system of equations have if the graph of the system is two lines which intersect? | One |

How many solutions does a system of equations have if the graph of the system is two lines which are parallel? | None |

How many solutions does a system of equations have if the graph of the system is two lines which are actually the same line? | Infinitely Many |

Two lines intersect at the point (3,5). How many solutions does this system of equations have? | One |

The following lines are graphed on the coordinate plane. y=3x + 4 y=3x - 8 How many solutions does this system of equations have? | None |

The following lines are graphed on the coordinate plane. y=2x -1 y=x + x -1 How many solutions does this system of equations have? | Infinitely Many |

The following lines are graphed on the coordinate plane. y=-4x +5 y=2x -7 How many solutions does this system of equations have? | One |

Two lines which have the same slope are graphed on the coordinate plane. One of them has a y-intercept of 10 while the other has a y-intercept of 2. How many solutions does this system of equations have? | None |

Two lines which have the same slope are graphed on the coordinate plane. They both pass through the point (9,4). How many solutions does this system of equations have? | Infinitely Many |

Two lines which have different slopes are graphed on the coordinate plane. They both pass through the point (-3,7). How many solutions does this system of equations have? | One |

Parallel lines are a system of equations with _____ solution(s). | No |

Intersecting lines are a system of equations with _____ solution(s). | One |

Coincident lines are a system of equations with _____ solution(s). | Infinitely Many |

Two lines which are directly on top of each other when graphed are a system of equations with _____ solution(s). | Infinitely Many |

When solving a system of equations algebraically, Bruno reaches a step in his algebra which says 7=6. The system of equations has ____ solution(s). | No |

When solving a system of equations algebraically, Mary reaches a step in her algebra which says 0=0. The system of equations has ____ solution(s). | Infinitely Many |

When solving a system of equations algebraically, Yesenia reaches a step in her algebra which says 0=x. The system of equations has ____ solution(s). | One |