# Thread: SYSTEM OF INEQUALITIES!!! HOW DO I SOLVE THIS?!

1. ## SYSTEM OF INEQUALITIES!!! HOW DO I SOLVE THIS?!

Y< 4x+3
y> -3x-3

I have no idea what I'm doing, I have no resources.

2. Hello, sukisaturn!

You've never done one of these before?
Then I'll give you a mini-lesson.

$\begin{array}{ccc}y &<& 4x+3 \\ y &>& \text{-}3x-3 \end{array}$

A one-variable inequality can be graphed on a number line.

For example: . $2x + 1 \:> \:5 \quad\Rightarrow\quad x \:>\:2$
Code:
      - - * - - - o = = = = =
0       2

A two-variable inequality is graph on a plane.

To graph: $y \:<\:4x + 3$
. . we graph the line: $y \:=\:4x + 3$

Because it says " $<$", we shade the region below the line.
Code:
          |   /::::
|  /::::
| /::::
|/:::::
*:::::
/|::::
- - *:+:-:- - -
/::|:::
/:::|::
/::::|::
|

To graph $y \:> \:\text{-}3x+3$
. . we graph the line: $y \:=\:\text{-}3x+3$
Because it says " $>$", we shade the region above the line.
Code:
          |
\::::|:::
\:::|::::
\::|::::
- - *:+:-:- - -
\|:::::
*:::::
|\:::::
| \::::
|  \

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

This shaded region represents billions of points with coordinates $(x,y)$
. . which satisfy both given inequalities.