# Finding Coordinates

• Oct 31st 2010, 09:19 AM
newgirl2012
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?
• Oct 31st 2010, 09:37 AM
wonderboy1953
Quote:

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.
• Oct 31st 2010, 02:19 PM
Soroban
Hello, newgirl2012!

Quote:

[I assume you want to graph this region.]

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

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

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

Code:

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

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

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

Code:

                  |             /////|/////             /////|/////             /////|/////       -------/////+/////--------             /////|/////             /////|/////             /////|/////         - - - - - + - - - -                   |                   |

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

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

Code:

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

Now consider the region that has been shaded three times.

Code:

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

That is the solution!