8: Algebraic Thinking
- Page ID
- 155314
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- 8-1 Variables
- 8-2 Equals Relation and Equations
- 8-3 Functions
- 8-4 Equations in a Cartesian Coordinate System
- * Module B: Using Real Numbers in Equations–online
- Chapter 8 Review
- 8.1: The Language of Algebra
- In algebra, we use letters of the alphabet to represent variables. The letters most commonly used for variables are x,y,a,b, and c .
- 8.4: Solving Equations with Variables and Constants on Both Sides
- In all the equations we have solved so far, all the variable terms were on only one side of the equation with the constants on the other side. This does not happen all the time—so now we will learn to solve equations in which the variable terms, or constant terms, or both are on both sides of the equation.
- 8.13: Systems of Equations - The Substitution Method
- Solving a system by graphing has its limitations. We rarely use graphing to solve systems. Instead, we use an algebraic approach. There are two approaches and the first approach is called substitution. We build the concepts of substitution through several examples and then conclude with a general four-step process to solve problems using this method.
- 8.14: System of Equations - The Addition Method
- The substitution method is often used for solving systems in various areas of algebra. However, substitution can get quite involved, especially if there are fractions because this only allows more room for error. Hence, we need an even more sophisticated way for solving systems in general. We call this method the addition method, also called the elimination method. We will build the concept in the following examples, then define a four-step process we can use to solve by elimination.
- 8.15: Applications with systems of equations
- We saw these types of examples in a previous chapter, but with one variable. In this section, we review the same types of applications, but solving in a more sophisticated way using systems of equations. Once we set up the system, we can solve using any method we choose. However, setting up the system may be the challenge, but as long as we follow the method we used before, we will be fine. We use tables to organize the parameters.