Final answer:
The elimination method is often utilized in systems of equations when one equation cannot be easily resolved for a single variable.
Step-by-step explanation:
The elimination method is used in place of substitution when one equation is not easily solved for a single variable. In the context of linear equations, the variable that can be chosen arbitrarily is referred to as the independent variable, and the variable that depends on it is called the dependent variable.
For example, in a linear equation of the form y = mx + b, x is the independent variable and y is the dependent variable. When using the elimination method, both equations in a system are manipulated to eliminate one of the variables, allowing the other variable to be easily solved for.