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Math Help - Finding Coordinates

  1. #1
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    Finding Coordinates

    I really don't understand this at all. It seems that when I look up the answer in the back of my math book it makes no sense!

    Here is what I am stuck on. This is an even problem so no answer but that doesn't help me either way!
    Could you do/explain how to get the following? I have my first chpter test on Tuesday and the way my teacher tries to explain it makes no sense but everyone else seems to understand her!

    x (great than equal to) -3
    y (greater than equal to) -2
    2x+y (less than equal to) -2

    Is it possible to do that actual (less than/equal to) sign?
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  2. #2
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    Quote Originally Posted by newgirl2012 View Post
    I really don't understand this at all. It seems that when I look up the answer in the back of my math book it makes no sense!

    Here is what I am stuck on. This is an even problem so no answer but that doesn't help me either way!
    Could you do/explain how to get the following? I have my first chpter test on Tuesday and the way my teacher tries to explain it makes no sense but everyone else seems to understand her!

    x (great than equal to) -3
    y (greater than equal to) -2
    2x+y (less than equal to) -2

    Is it possible to do that actual (less than/equal to) sign?
    "Is it possible to do that actual (less than/equal to) sign?" Yes, using LaTex.

    What the problem is asking for is the common domain among the three inequalities, then work out what the range would be.
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  3. #3
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    Lexington, MA (USA)
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    Hello, newgirl2012!

    [I assume you want to graph this region.]

    . . \begin{array}{cc}(1) & x \:\ge\: -3 \\<br />
 (2) & y \:\ge\: -2 \\ (3) & 2x+y \:\le\: -2 \end{array}

    (1)\;x \:\ge\:-3

    Graph the vertical line x = \text{-}3
    Then shade region to the right of that line.


    Code:
              :////   |
              :////   |
              :////   |
              :////   |
              :////   |
      --------:////---+------
              :////   |
              :////   |
              :////   |

    (2)\;y \,\ge\,\text{-}2

    Graph the horizontal line y = \text{-}2
    Then shade the region above that line.


    Code:
                      |
                 /////|/////
                 /////|/////
                 /////|/////
          -------/////+/////--------
                 /////|/////
                 /////|/////
                 /////|/////
            - - - - - + - - - -
                      |
                      |


    (3)\;2x + y \:\le\:-2

    Graph the line y\:=\:-2x-2
    . . It has intercepts (-1,\,0)\text{ and }(0,-2)
    Then shade the region below that line.


    Code:
            :\        |
            ::\       |
            :::\      |
            ::::\     |
            :::::\    |
      ------::::::*---+--------
            :::::::\  |
             :::::::\ |
             ::::::::\|
              ::::::::*
               :::::::|\
                ::::::|:\
                ::::::|::\



    Now consider the region that has been shaded three times.


    Code:
             \        |
              *       |
              :\      |
              ::\     |
              :::\    |
           ---::::\---+------
              :::::\  |
              ::::::\ |
              :::::::\|
              * - - - *
                      |

    That is the solution!
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