# Week 15 – Solving Systems

What is a system?

In math, a system is a two or more linear equations involving the same set of variables. Meaning each system must have x and y in the equation or what other variables you are using for the equation. One example of a system is this: How to solve a system?

There are many different ways to solve a system such as grafting, substitution and elimination. However, I am going to focus only one of the ways to solve systems substitution. What is the method of substitution? The substitution method is used to eliminate one of the variables by replacement when solving a system of equations. You can think of it as “grabbing” what one variable equal from one equation and “plugging/substituting” it into the other equation. This method works best when one of the linear equations have a variable that does not have a coefficient (so it is all by itself). You can still use it with variables that all have coefficients but it will probably end up in fractions.

The first step is you are going to isolate one of the variables in one of the linear equations, try to make sure it is the best choice (the easiest). Next, with the isolated equations, you are going to “plug” this equation (“substitute it”) for the variable you choose in the other equation, and solve for the other variable. This will leave you with an equation with only one variable. After you are done solving and you have an answer. You are going to take the answer and plug this variable value back into either equation and solve for the other variable that you started with. Lastly, you can verify your answer by inputting the variables that you have come up with into the original equations.

For Example: 