# Thread: Figuring out x and y values in a constraint

1. ## Figuring out x and y values in a constraint

I need to know how to find an x and y value to graph for the constraint

3 < 3x + y < 12

I know how to do something like: 3x -2y > -6

where I set either x or y = to 0 and end up with x = 2, y = 3

However, I do not know how to do 3 < 3x + y < 12

2. Take a look at this image.

It shows all possible values (well, not ALL, that would require infinite space) of X and Y that satisfy the equation

3 < 3x+y < 12

From there I'm not sure what you are supposed to answer? Your question isn't very clear.

Notice that the equations of the two red lines are

y=-3x+3

and

y=-3x+12

so

-3x+3 < y < -3x+12

3. That is all I needed to know.

Thank you so much!

4. Hello, pungakitty!

Sorry, the work you showed makes no sense . . .

Graph the inequality: . $3 \:<\: 3x + y \:<\: 12$

We have two inequalties:

. . $\begin{array}{ccc}3x + y &<& 12 \\ 3x + y &>& 3 \end{array}$

Solve for $y\!:\;\;\begin{array}{cccc}y &<& -3x + 12 & [1] \\ y & > &-3x+3 & [2] \end{array}$

Then graph the two inequalties.

$[1]\;\;y \;<\;-3x+12$

Graph the line: . $y \:=\:-3x+12$
. . and shade the region below the line.

Code:
          |
:\   |
::\  |
:::\ |
::::\|
:::::*12
:::::|\
:::::|:\
:::::|::\
:::::|:::\
:::::|::::\
:::::|:::::\
:::::|::::::\
:::::|:::::::\
:::::|::::::::\
- -:-:-:+:-:-:-:-:\ - - -
:::::|::::::::::\
:::::|:::::::::::\
:::::|::::::::::::\
|

$[2]\;\;y \;>\;-3x+3$

Graph the line: . $y \:=\:-3x+3$
. . and shade the region above the line.

Code:
          |
:::::|::::::::::::::::
:::::|::::::::::::::::
:::::|::::::::::::::::
:::::|::::::::::::::::
:::::|::::::::::::::::
:::::|::::::::::::::::
\:::|::::::::::::::::
\::|::::::::::::::::
\:|::::::::::::::::
\|::::::::::::::::
3*::::::::::::::::
|\:::::::::::::::
| \::::::::::::::
- - - + -\-:-:-:-:-:-:- - -
|   \::::::::::::
|    \:::::::::::
|     \::::::::::
|

The solution is the region common to both shadings.

Code:
          |
:\   |
::\  |
:::\ |
::::\|
:::::*12
:::::|\
:::::|:\
\:::|::\
\::|:::\
\:|::::\
\|:::::\
3*::::::\
|\::::::\
| \::::::\
- - - - + -\-:-:-:\ - - -
|   \::::::\
|    \::::::\
|     \::::::\
|      \::::::\
|