yhteenlaskumenetelmä

Yhteenlaskumenetelmä, often translated as the addition method or elimination method, is a common technique used to solve systems of linear equations. The fundamental principle behind this method is to manipulate one or both equations in a system so that when the equations are added together, one of the variables cancels out. This leaves a single equation with only one unknown variable, which can then be solved directly.

To apply the yhteenlaskumenetelmä, one typically starts by examining the coefficients of the variables in each equation. If the coefficients for a particular variable are opposites (e.g., 2x and -2x), adding the equations directly will eliminate that variable. If the coefficients are not opposites, one or both equations can be multiplied by a constant to make them opposites. For instance, if one equation has 3x and the other has 2x, multiplying the first equation by -2 and the second by 3 would result in -6x and 6x, which would then cancel upon addition.

Once one variable has been eliminated and its value is found, this value is substituted back into one of the original equations to solve for the remaining variable. The solution to the system of equations is then the pair of values found for both variables. This method is particularly efficient when the coefficients are already aligned for elimination or can be easily adjusted.