yhteenlaskumenetelmällä

Yhteenlaskumenetelmä is a Finnish term that translates to "addition method" or "elimination method" in English. It refers to a technique used to solve systems of linear equations. The core idea behind this method is to manipulate one or both equations in the system such that when the equations are added or subtracted, one of the variables cancels out. This leaves a single equation with only one variable, which can then be solved directly.

To apply the addition method, the coefficients of one variable in both equations must be opposites. If they are not, one or both equations are multiplied by a constant to make the coefficients opposites. For example, if one equation has a +3y term and the other has a -3y term, adding the two equations will eliminate the y variable. Similarly, if the coefficients are the same (e.g., +3y in both), subtracting one equation from the other will eliminate the variable.

Once a variable has been eliminated and the remaining single-variable equation is solved, the value of that variable is substituted back into one of the original equations. This allows for the calculation of the value of the second variable. The solution to the system of equations is then the pair of values (x, y) that satisfies both original equations. The addition method is particularly efficient when the equations are already arranged with like terms aligned vertically.