When solving a system of equations, the method to use largely depends on the nature of the equations and the desired outcome. There are primarily three methods: substitution, elimination, and graphing. The substitution method is useful when one equation can be manipulated to solve for one variable and substituted into the other equation. Elimination is preferable when adding or subtracting two equations allows for the elimination of one variable. This method proves effective when coefficients of variables in both equations are opposites or can be easily manipulated to become opposites. Lastly, graphing can be employed when visualizing the solutions is required or when dealing with linear equations. Depending on the given equations, their complexity, and the desired way of presenting the solutions, a method is chosen accordingly, with each method having its own advantages and considerations.
