# What is meant by a system of inequalities?

##### 1 Answer
Aug 29, 2015

A system of inequalities is a set of inequalities that you deal with all at once.

#### Explanation:

Solving a system of inequalities means graphing each individual inequality and then finding the overlaps of the various solutions.

EXAMPLE:

Solve the following system:

2x – 3y ≤ 12
x + 5y ≤ 20
$x > 0$

Solution:

Step 1: Solve as many of the inequalities as possible for $y$.

y ≥ 2/3x – 4
y ≤ – 1/5 x + 4
$x > 0$

Step 2. Graph each inequality, shading the area that satisfies the condition.

(a) Graph y ≥ 2/3x – 4

(b) Graph y ≤ – 1/5x + 4

(c) Graph $x > 0$

This is a ">" inequality, so you use a dashed line to show that $x = 0$ is not part of the solution.

(d) Shade the area that satisfies all the inequalities.

And you have solved your system of inequalities.