Steps To Solving A Linear System In Three Variable

Steps to solving a linear system in three variables
Tiffany Mclean
MTH/209
March 6, 2012

Linear equations are intimidating when you first start to learn about them, but when you add in three linear system equations with three different variables, they can become overwhelming. When solving a linear system with three variables, students must understand the four-step process to find the solutions. These four steps are used to solve linear systems with three variables, and must be followed step by step. By following these steps, students can identify the answer for all three variables, but students must understand that not all systems have just one solution or a solution at all. Solutions may have infinitely many solutions, one solution, or no solution.
Identify four-steps to solving a linear system in three variables
The best way to solve a linear equation with three variables is by using the elimination method. To fully explain how to solve this type of linear system it would be nine steps. But here it is broken down into four steps. Choose which variable you want to eliminate; the coefficients of the variables must be exact opposites. You will only use two equations at one time. Second add the two equations together to cancel out your variables. IF nothing cancels than you have to multiply one or both of your equations by a number that will create an equal. Then for the unused equation and any of the other two equations repeat steps above. By this time you should have solved for two variables. Take the two variables you have solved for and put into any equation and solve for you remaining variable rather it be x, y, or z. Then the fourth step is to check put your tripled pair into all three equations and make sure they are correct.
Do these steps have to be in a certain order?
When solving a linear equation with three variables there is a certain