Solving a System of Linear Equations by Elimination
The elimination method (also called the addition method) is the third technique for solving a system of two linear equations in two variables, joining the graphing method and the substitution method. Like substitution, it reduces a system of two equations with two unknowns to a single equation in one variable, but it reaches that one-variable equation through a different algebraic approach. The procedure follows seven steps:
- Write both equations in standard form. If any coefficients are fractions, clear them.
- Make the coefficients of one variable opposites. Decide which variable to eliminate, then multiply one or both equations by appropriate constants so that the chosen variable's coefficients are opposites (e.g., and ).
- Add the equations resulting from Step 2 to eliminate one variable.
- Solve for the remaining variable.
- Substitute the solution from Step 4 into one of the original equations, then solve for the other variable.
- Write the solution as an ordered pair.
- Check that the ordered pair is a solution to both original equations.
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Ch.5 Systems of Linear Equations - Elementary Algebra @ OpenStax
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