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Solving a System of Linear Equations by Elimination
To solve a system of two linear equations by elimination, follow this seven-step procedure:
- Write both equations in standard form. If any coefficients are fractions, clear them first.
- Make the coefficients of one variable opposites. Decide which variable to eliminate, and multiply one or both equations by carefully chosen constants so that the coefficients of that variable become opposites.
- Add the two resulting equations to eliminate that variable.
- Solve the new equation for the remaining variable.
- Substitute this solution back into one of the original equations and solve for the other variable.
- Write the final solution as an ordered pair .
- Check the ordered pair by substituting its coordinates into both original equations to verify that each yields a true statement.
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Intermediate Algebra @ OpenStax
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