What is elimination in algebra?

Elimination is a method for solving a system of two or more algebraic equations by transforming the system so that one of the variables cancels out. It is sometimes called the addition method because it involves adding equations together.

An example of a set of linear equations that can be solved using the elimination method is: 4x + 2y = 14 and 2x - y = 1. To create coefficients that cancel each other out, the terms of the second equation are multiplied by 2, producing the equation 4x - 2y = 2. Adding the two equations together causes 2y and -2y to cancel each other out, leaving 8x = 16, or x = 2. Plugging an x value of 2 back into the original equation 2x - y = 1 leads to the solution y = 3.