Solving Linear Systems via Elimination in 2026
The Elimination Method (also known as the Addition Method) solves systems of linear equations by multiplying one or both equations by non-zero constants so that the coefficients of one variable become additive opposites, eliminating that variable when the equations are summed.
Elimination Steps Overview
- 1Align Terms in Standard Form: Write both equations as $ax + by = c$.
- 2Choose Variable to Eliminate: Multiply one or both equations to produce opposite coefficients.
- 3Add Equations: Sum matching columns to eliminate the chosen variable.
- 4Solve One-Variable Equation: Find the value of the remaining variable.
- 5Back-Substitute: Plug the found value back into either original equation to find the second variable.