Poistomenetelmä

Poistomenetelmä, often translated as "removal method" or "elimination method," is a fundamental concept in mathematics, particularly in algebra. It refers to a technique used to solve systems of linear equations. The core idea behind the poistomenetelmä is to systematically eliminate one or more variables from the equations by adding or subtracting multiples of the equations from each other. This process transforms the original system into a simpler one with fewer variables, which can then be solved more easily.

To apply the poistomenetelmä, one typically manipulates the equations so that the coefficients of a chosen variable are either the same or additive inverses. For instance, if one equation has `2x` and another has `-2x`, adding the two equations will eliminate `x`. If the coefficients are not directly opposite, one or both equations can be multiplied by a constant to achieve this. Once a variable is eliminated, the resulting equation, containing only the remaining variables, is solved. This process can be repeated for any remaining variables until a single variable's value is found. Back-substitution is then used to find the values of the other variables. The poistomenetelmä is a systematic and efficient way to solve systems of linear equations, especially when dealing with larger systems.