A technique employed to solve systems of equations involves strategically manipulating the equations to remove one variable. This manipulation typically involves multiplying one or both equations by constants, followed by either adding or subtracting the equations to cancel out a chosen variable. Once one variable is eliminated, the resulting equation can be solved for the remaining variable. Subsequently, the value of the solved variable is substituted back into one of the original equations to determine the value of the eliminated variable. For example, given two linear equations with two unknowns, this approach aims to create a new equation with only one unknown, simplifying the solution process.
This process offers a systematic way to tackle systems of equations, ensuring accuracy and efficiency in finding solutions. Its adaptability to various equation types and its foundational role in linear algebra contribute to its widespread use in diverse fields, including mathematics, physics, engineering, and economics. Historically, methods for solving systems of equations have evolved over centuries, with this particular technique solidifying as a core principle in algebraic problem-solving.
