Additionsverfahrens

Additionsverfahrens, also known as the addition method or elimination method, is a common technique used in algebra to solve systems of linear equations. The core principle is to manipulate one or both equations in the system so that when they are added together, one of the variables cancels out, or is eliminated. This results in a single equation with only one variable, which can then be easily solved.

To apply the additionsverfahrens, you typically start by ensuring that the coefficients of one of the variables in both equations are opposites. For example, if one equation has a $+3y$ term and the other has a $-3y$ term, adding the equations will eliminate the $y$ variable. If the coefficients are not opposites, you can multiply one or both equations by a suitable constant to make them so. Once the variable is eliminated, you solve the remaining equation for the other variable. The value obtained is then substituted back into one of the original equations to find the value of the eliminated variable, thus providing the solution to the system. This method is particularly useful when dealing with equations where variables are not easily isolated for substitution.