asendustehnika

Asendustehnika, literally "substitution technique" in Estonian, is a problem-solving method used across disciplines, most prominently in mathematics. It refers to the replacement of a variable, expression, or object by an equivalent one to simplify a task, solve an equation, or reveal relationships between quantities. In Estonian educational materials, asendustehnika is taught as a key strategy for reducing complex problems to more manageable forms through substitution.

In algebra, the method typically proceeds by solving one equation for a chosen variable and substituting the resulting expression into the remaining equations. For example, in the system x + y = 5 and 2x - y = 1, solving the first for y gives y = 5 - x, which substituted into the second yields 2x - (5 - x) = 1. This leads to x = 2 and y = 3. The technique emphasizes expressing unknowns in terms of knowns and removing variables step by step.

Substitution is also a foundational idea in calculus and analysis, where substitution methods such as u-substitution transform integrals to simpler forms, often by changing the variable of integration. In programming and computer algebra, substitution features prominently in symbolic manipulation, pattern replacement, and evaluation of expressions.

Because terminology and emphasis vary by curriculum, asendustehnika is often described simply as the substitution method or technique in Estonian sources. It is part of the broader problem-solving repertoire that includes elimination, factoring, and other algebraic strategies.