# How do you graph the system of linear inequalities y> -3x and x<=5y?

Feb 13, 2018

#### Explanation:

Given:

color(red)(y >= -3x and color(red)(x <= 5y

Let color(red)(y >= -3x " " Inequality.1

Let color(red)(x <= 5y " " Inequality.2

Consider:

$x \le 5 y$

Switching sides, we get

$5 y \ge x$

We will divide both sides by 5:

$\frac{5 y}{5} \ge \frac{x}{5}$

Simplify:

$\frac{\cancel{5} y}{\cancel{5}} \ge \frac{x}{5}$

$\Rightarrow y \ge \frac{x}{5}$ Inequality.3

We will consider:

color(blue)(y >= -3x " " Inequality.1 and

color(blue)(y >= x/5 " " Inequality.3

for graphing.

Please refer to the image of the graph of the inequality color(blue)(y >= -3x " " below:

Please refer to the image of the graph of the inequality color(blue)(y >= x/5 " " below:

The Solution to the system of inequalities will be the area where the Shaded area from each inequality overlap one
another.

Please refer to the graph below to view the solutions:

Notice that we have a dashed line to show that it does not include values for color(green)(y = (-3x), color(blue)(AA x in RR