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Math Help - SYSTEM OF INEQUALITIES!!! HOW DO I SOLVE THIS?!

  1. #1
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    Post SYSTEM OF INEQUALITIES!!! HOW DO I SOLVE THIS?!

    Y< 4x+3
    y> -3x-3

    I have no idea what I'm doing, I have no resources.
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  2. #2
    Super Member

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    Hello, sukisaturn!

    You've never done one of these before?
    Then I'll give you a mini-lesson.


    \begin{array}{ccc}y &<& 4x+3 \\ y &>& \text{-}3x-3 \end{array}

    A one-variable inequality can be graphed on a number line.

    For example: . 2x + 1 \:> \:5 \quad\Rightarrow\quad x \:>\:2
    Code:
          - - * - - - o = = = = =
              0       2

    A two-variable inequality is graph on a plane.


    To graph:  y \:<\:4x + 3
    . . we graph the line: y \:=\:4x + 3

    Because it says " <", we shade the region below the line.
    Code:
              |   /::::
              |  /::::
              | /::::
              |/:::::
              *:::::
             /|::::
        - - *:+:-:- - -
           /::|:::
          /:::|::
         /::::|::
              |

    To graph y \:> \:\text{-}3x+3
    . . we graph the line: y \:=\:\text{-}3x+3
    Because it says " >", we shade the region above the line.
    Code:
              |
         \::::|:::
          \:::|::::
           \::|::::
        - - *:+:-:- - -
             \|:::::
              *:::::
              |\:::::
              | \:::: 
              |  \

    The final answer is the region that has been shaded twice.
    Code:
              |
              |  /::
              | /:::
         \    |/::::
          \   *:::::
           \ /|:::::
        - - *:+:-:-:- -
           / \|:::::
          /   *:::::
         /    |\::::
              | \::: 
              |  \::
              |

    This shaded region represents billions of points with coordinates (x,y)
    . . which satisfy both given inequalities.

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