We want to determine if 2x+8y=20 and 3x+9y=50 are parallel, intersect, or intersect and are perpendicular:

2x + 8y = 20

8y = -2x + 20

8y |

8 |

= |

-2x + 20 |

8 |

y = -0.25x + 2.5

Therefore, the slope (gradient) of line equation 1 = -0.25

3x + 9y = 50

9y = -3x + 50

9y |

9 |

= |

-3x + 50 |

9 |

y = -0.33x + 5.6

Therefore, the slope (gradient) of line equation 2 = -0.33

-0.25x + 2.5 = -0.33x + 5.6

-0.25x - -0.33x = 5.6 - 2.5

+ 0.333x = 3.6

x = 3.6/ + 0.333

x = 36.

Now that we have x, plug it into equation 1 to find y

y = -0.25 * (36.) + 2.5

y = -9.7 + 2.5

y = -6.6667

Therefore, our intersection point = (36., -6.6667)

Slope 1 * Slope 2 = -0.25 * -0.33 = 0.333

Since the product of the 2 slopes <> - 1, the lines are not perpendicular

Since the slopes are different and the lines cross, the systems are independent

In order for a system to be dependent, the slopes and y-intercept must be the same. This is not the case

In order for a system to be inconsistent, the slopes must be the same and y-intercept must different. This is not the case

tan(θ) = | m_{2} - m_{1} |

1 + m_{2}m_{1} |

tan(θ) = | -0.33 --0.25 |

1 + -0.33 *-0.25 |

tan(θ) = | -0.333 |

1 + 0.333 |

tan(θ) = | -0.333 |

3 |

tan(θ) = -0.077

θ = -4.3987