A lot of people have been interested in a general Algebra 1 study guide that provides a concise look at the most basic ideas that will be asked about on tests, especially in the first half of an Algebra 1 course. So to help these people out, we’re going to look at all of the most basic ideas in a way that will help you to make sure you understand the fundamentals of Algebra 1. If you see a concept that you don’t think you understand, check out the sections of this website specific to that topic.

**Solving Linear Equations**

The main thing you’re going to be tested on here on the vast majority of Algebra 1 tests is your ability to solve so-called two-step equations. You’re going to want to take an equation that looks something like 2x – 3 = 5 and get the answer of x = 4. The main way to do this is to “undo” each of the operations that keeps 2x – 3 = from looking like x =. So in this example, you would add 3 and then divide by 2. That means you’ll also add 3 to the right-hand side of the equation to get 8, and then divide by 2 to get 4.

**Graphing Linear Equations**

Be able to put equations into the slope-intercept form of y = mx + b. Know how to find the slope of an equation when you’re given two points, and know how to find the equation of a line if you’re given two points. Finally, know how to graph a linear equation once you’re given the equation. (Hint: Start by plotting the y-intercept, then find one more point using the slope and connect the two points with a line.)

**Solving Systems of Equations**

You’re going to need to know the three possible outcomes of a linear system of two equations (one solution, infinite solutions, no solutions) and how each of these happen (one intersection, they’re the same line, the lines are parallel, respectively). You’re also going to need to be able to demonstrate the ideas of solving by substitution, solving by elimination, and solving by graphing. On this website, we show examples of each of these methods, as well as a simple method for actually solving the systems.

You can also download this as a PDF file here:

Download: Algebra 1 Study Guide eBook (.zip file)