liitmisvõtte

Liitmisvõtte, often translated as the "addition method" or "elimination method" in English, is a fundamental algebraic technique used to solve systems of linear equations. Its primary purpose is to eliminate one or more variables from the system by adding or subtracting multiples of the equations. This process reduces the number of variables, making the remaining equations easier to solve.

The core principle behind the liitmisvõtte is that if two equations are equal, then adding or subtracting equivalent expressions from both sides of these equations will maintain the equality. To apply the method effectively, one typically manipulates the coefficients of the variables in the equations so that when the equations are combined, the coefficients of one variable become opposites (e.g., +3x and -3x) or identical. If they are opposites, adding the equations will cause that variable to cancel out. If they are identical, subtracting one equation from the other will achieve the same result.

Once a variable has been eliminated, the resulting single-variable equation can be solved directly. The value of this solved variable is then substituted back into one of the original equations to find the value of the other variable. This systematic approach ensures that a unique solution to the system of linear equations is found, provided a unique solution exists. The liitmisvõtte is a powerful tool for solving systems of any size, though it becomes more complex with a greater number of variables.