A system of linear equations is when you have two or more linear equations that can only be solved as a group and cannot be solved individually. The reason these equations cannot be answered separately is that they have more than one variable. The rule of thumb is for every variable in the problem you need to have an equation to find its value. Take the following equation:
The equation has four variables, x, y, z, and w. Because the above equation has four variables, we cannot find the values of these four variables with only this one equation. To calculate the values of all of these variables, you will need three additional equations.
In a system of linear equations, the value of a variable is the same throughout the entire system. This means that if we have a system of three equations with three variables, x, y, and z, the value of x is the same through all three equations.
There are several methods to solve a system of linear equations they are: