Elimination Method Equation Solver

Understanding Elimination Method

The elimination method is a technique used to solve systems of linear equations. It works by manipulating the equations to eliminate one of the variables, making it possible to solve for the other. For a system of two equations, like the ones above (a₁x + b₁y = c₁ and a₂x + b₂y = c₂), the goal is to make the coefficients of either x or y the same (or additive inverses) in both equations. This can be achieved by multiplying one or both equations by a constant. Once the coefficients of one variable are opposites, adding the equations will eliminate that variable, leaving an equation in just one variable that can be easily solved. After finding the value of one variable, substitute it back into either of the original equations to solve for the other variable. This method is effective for solving systems of linear equations by hand or programmatically.

• Useful for solving linear systems in algebra and various applications.
• Helps in understanding the relationships between variables in linear equations.