# Thread: [SOLVED] Algebra (Cumulative Review) Linear Systems and Inequalities

1. ## [SOLVED] Algebra (Cumulative Review) Linear Systems and Inequalities

Ok, I have no clue how to do these, its a linear inequality system.

{y≤1/5x+12/5
{y≥-x
{y≥2x-3
Btw, they are all in one bracket. How do I write equations?

2. Hello, jscalalamoboy!

No clue ??

Okay, just this once . . . for you . . .

$\displaystyle \begin{Bmatrix}y \:\leq \:\frac{1}{5}x + \frac{12}{5} \\ y \:\geq \:-x \\ y\:\geq\:x-3 \end{Bmatrix}$

You need to graph the inequalities and shade the required region.

Graph the line: .$\displaystyle y \:=\:\frac{1}{5}x + \frac{12}{5}$
. . . It has y-intercept $\displaystyle \frac{12}{5}$ and slope $\displaystyle \frac{1}{5}$

The inequality is $\displaystyle \leq$ . . . Shade the region below the line.
Code:
                |                   *;;
|               *:::::;
|           *::::::::
|       *::::::::::
|   *::::::::::::
*::::::::::::::
*:::|::::::::::::
*:::::::|::::::::::
- *:-:-:-:-:-:+:-:-:-:- - - - - - -
::::::::::::|::::::
::::::::::::|::::
|

Graph the line: .$\displaystyle y \:=\:-x$
. . It has y -intercept 0 and slope -1.

The inequality is $\displaystyle \geq$ . . . Shade the region above the line.
Code:
    *:::::::::::|:::
*:::::::::|::::
*:::::::|:::::
*:::::|::::::
*:::|:::::::
*:|::::::::
- - - - - - *:-:-:-:-:- -
| *::::::::
|   *:::::::
|     *::::::
|       *
|

Graph the line: .$\displaystyle y \:=\:2x-3$
. . It has y-intercept -3 and slope 2.

The inequality is $\displaystyle \geq$ . . . Shade the region above the line.
Code:
                |:::::::::::*
|::::::::::*
:|:::::::::*
::|::::::::*
:::|:::::::*
::::|::::::*
- - - -:-:-:+:-:-:* - - -
::::::|::::*
:::::::|:::*
::::::::|::*
:::::::::|:*
::::::::::|

The solution is the triangular region common to all three.
And we are usually expected to find the coordinates of the vertices.
Code:
                |
|           o(3,3)
|       *::*
|   *:::::*
*::::::::*
(-2,2)o:::|:::::::*
*:|::::::*
- - - - - - - - *:-:-:* - - - - - - -
| *::*
|   o(1,-1)
|

3. how do you do those fun graphs soroban?

4. YEAH! Thanks bro! I PASSED! WHOOOOOO!