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

• Nov 27th 2008, 09:04 AM
sukisaturn
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.
• Nov 27th 2008, 10:28 AM
Soroban
Hello, sukisaturn!

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

Quote:

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

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

For example: .$\displaystyle 2x + 1 \:> \:5 \quad\Rightarrow\quad x \:>\:2$
Code:

      - - * - - - o = = = = =           0      2

A two-variable inequality is graph on a plane.

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

Because it says "$\displaystyle <$", we shade the region below the line.
Code:

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

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

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

Code:

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

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