Occasionally, we need to find a point where two linear equations are both satisfied.
There are several approaches one can take. Which one you select may depend on how much easier finding a solution with that method is over other methods.
While any of the techniques is allowed for any problem, it is wise to reduce the amount of work. Selecting the most cumbersome technique can allow more careless errors to occur. Which technique is the more cumbersome is often a matter of the numbers in a particular problem.
Another reason for learning all of the techniques is to develop the skills necessary for solving nonlinear equations. This happens in College Algebra. In nonlinear system of equation problems often there is a technique that works that must be selected. So, always prepare for what is coming.