Elimination Method - Steps, Techniques, and Examples - The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day
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The elimination method is one of the most powerful ways to solve systems of equations. Instead of solving for one variable first like substitution, elimination lets you "cancel out" one variable completely by adding or subtracting the equations. The key is making the coefficients of one variable opposites so they eliminate each other when combined. Start by looking at the coefficients and deciding which variable to eliminate. In this system, notice that the y-coefficients are already opposites:
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