# Understanding the System of Inequalities

In the world of mathematics, a system of inequalities is a set of two or more inequalities that are related to each other. Understanding how these systems work can help you solve complex equations, which can be a valuable skill for many professions. In this article, we’ll discuss what a system of inequalities is and how it can be used.

## What is a System of Inequalities?

A system of inequalities is a set of two or more inequalities that are related to each other. This means that the solution to one inequality also solves the other inequalities. For example, if you have two equations, one that states x>3 and one that states x<10, then the solutions of both these equations would be any number between 3 and 10.

## What is an Inequality?

An inequality is a statement that compares two values. It is similar to an equation, but instead of using an equals sign (=) it uses symbols such as greater than (>), less than (<), or not equal to (!=). For example, if you have the inequality x > 10, this means that x is greater than 10. If x is less than 10, then the inequality is not true.

## How to Solve a System of Inequalities

Solving a system of inequalities is a multi-step process. First, you need to identify the variables in the equation and the type of inequality. Next, you create a graph for each inequality and draw a line for the boundary that the solutions have to stay within. Once you have the graph, you can then identify the solutions that are true for each inequality.

### Which System of Inequalities is Shown?

Once you understand what a system of inequalities is and how to solve them, you can then identify which system of inequalities is shown. This can be done by looking at the equations and the type of inequalities they use. For example, if you have two equations that use greater than (>), then the system of inequalities is shown as x > 3 and x < 10. In conclusion, a system of inequalities is a set of two or more inequalities that are related to each other and have solutions that are within a certain boundary. Understanding how these systems work can help you solve complex equations and identify which system of inequalities is shown.