# How do you graph the system of linear inequalities y> -5, x>3 and 2x+y<13?

Feb 28, 2018

The dark blue triangle is the solution

#### Explanation:

You must represent each graph in the euclidean plane

$y \succ 5$ are all points of plane having second coordinate bigger than -5

$x > 3$ are all the points of plane having first coordinate bigger than 3

Finally, $2 x + y < 13$ are the points of plane below the line represented by $y = 13 - 2 x$

The interception points can be calculated by

$y = 13 - 2 x$
$y = - 5$

So, $- 5 = 13 - 2 x$ hence $x = - 9$ Intercep. Point $\left(- 9 , - 5\right)$

The other two points can be found in the same way

The intersection of three areas is the searched solution