There are times when multiple algebraic or linear equations will have the same set of unknown variables. There are many circumstances where the values will satisfy each of the equations in the series. This is often solved through the method of substitution where you solve for a variable in one of the equations in the set and plug that value into one of the other available equations. When that method does not work to meet the needs of each equations you can graph the equations and see where they agree towards a select number of points or in better term intersect. These types of problems are helpful for many different real-world comparisons and they often fit them nicely. These sheets work on the concept of systems. You will be given systems of two equations and you are tasked with balancing the system. Some worksheets also ask you to start identifying the variables through the use of graphs on x-y axes. This set contains all introductory material, practice questions, reviews, longer exercise sheets, and quizzes. Answers are provided for everything, so that will definitely help you out.

The first goal you have is to identify the location of like variables in the system. Once you identify those, the rest will just fall into place for you. The work we have created will spend a great deal of time working on the substitution method for solving systems. As you advance into geometry, we will highlight the uses of graphing to find matching points of intersection. Systems have one of three possibilities. Either there is no solution which means a system does not exist. That is termed an inconsistent state. There can be a perfect option where only one solution exists or you can enter a phase where infinitely solutions exist and these conditions are called a consistent state. Use these worksheets to demonstrate and practice the skills needed to understand how to graph and solve systems of equations.