How Do You Solve a System of Inequalities by Graphing?

How Do You Solve a System of Inequalities by Graphing?

Note:

There are many different ways to solve a system of inequalities. In this tutorial, you'll see how to solve such a system by graphing both inequalities and finding their intersection. Check it out!

Keywords:

  • problem
  • inequality
  • line
  • linear inequality
  • border
  • shading
  • graphical
  • graph
  • system of inequalities
  • 2 inequalities
  • region
  • overlap
  • independent
  • consistent
  • half plane
  • 2 equations
  • 2 unknowns
  • 2 variables

Background Tutorials

  • Graphing Linear Inequalities

      • How Do You Graph a Greater Than Inequality on the Coordinate Plane?How Do You Graph a Greater Than Inequality on the Coordinate Plane?

      How Do You Graph a Greater Than Inequality on the Coordinate Plane?

      Graphing inequalities on the coordinate plane is not as difficult as you might think, especially if you know what to do! In this tutorial, you'll see the steps you need to follow to graph an inequality.

      • What's a Half-Plane?What's a Half-Plane?

      What's a Half-Plane?

      If you graph an inequality on the coordinate plane, you end up creating a boundary that cuts the coordinate plane in half. Each of these halves is called a half-plane. Learn about half-planes by watching this tutorial!

  • Systems of Linear Inequalities

      • What's a System of Linear Inequalities?What's a System of Linear Inequalities?

      What's a System of Linear Inequalities?

      A system of equations is a set of equations with the same variables. A system of inequalities is almost exactly the same, except you're working with inequalities instead of equations! To solve such a system, you need to find the variable values that will make each inequality true at the same time. This tutorial will introduce you to systems of inequalities.

  • Evaluating Expressions

      • What is a Variable?What is a Variable?

      What is a Variable?

      You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

  • Ordered Pairs and The Coordinate Plane

      • What is the Coordinate Plane?What is the Coordinate Plane?

      What is the Coordinate Plane?

      You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.

  • Solving Inequalities by Dividing

      • What's the Division Property of Inequality?What's the Division Property of Inequality?

      What's the Division Property of Inequality?

      Ever wondered what rules you're allowed to follow when you're working with inequalities? Well, one of those rules is called the division property of inequality, and it basically says that if you divide one side of an inequality by a number, you can divide the other side of the inequality by the same number. However, you have to be very careful about the direction of the inequality! Watch the tutorial to see how this looks in terms of algebra!

Further Exploration

  • Solving Systems of Equations

      • How Do You Solve a System of Equations by Graphing?How Do You Solve a System of Equations by Graphing?

      How Do You Solve a System of Equations by Graphing?

      There are many different ways to solve a system of linear equations. In this tutorial, you'll see how to solve a system of linear equations by graphing both lines and finding their intersection. Take a look!