1. ## 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?

2. 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.

3. Hello, newgirl2012!

[I assume you want to graph this region.]

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

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

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!