Real math help.
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!
Background Tutorials
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Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
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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.
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Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
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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!
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Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
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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!
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Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
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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.
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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.
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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!
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Further Exploration
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Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
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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!
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