igualación

Igualación is a method used to solve systems of linear equations. It is one of several techniques, alongside substitution and elimination, that can be employed to find the values of variables that satisfy all equations in the system simultaneously. The core principle of the igualación method is to isolate the same variable in both equations of the system. Once this is done, the expressions that are equal to that isolated variable are then set equal to each other, forming a new equation with only one variable. This single-variable equation can then be solved directly. After determining the value of this variable, it is substituted back into one of the original equations (or one of the isolated expressions) to find the value of the other variable. The term "igualación" itself is Spanish for "equalization" or "equating," which accurately describes the central step of setting two expressions equal to each other. This method is particularly useful when the coefficients of one variable in both equations are simple or when it is straightforward to isolate a particular variable. While effective, it may become cumbersome with complex equations or equations where isolating a variable leads to fractions.