Finding Coordinates

**newgirl2012** · October 31st 2010, 09:19 AM

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?

**wonderboy1953** · October 31st 2010, 09:37 AM

Originally Posted by newgirl2012

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.

**Soroban** · October 31st 2010, 02:19 PM

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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