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I don't understand what you are asking?
suppose you have a specific system to solve, like
then you can rewrite the first equation
\[2x+3y=13\] as an "equivalent" equation
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thank you @satellite73 as usual you are amazing. you are so awesome. i love you
the purpose for doing that, is that now you have the same "coefficient' for the \(y\) term, which means when you add the two equations
\[4x+6y=26\]\[x-6y=-1\] you get
\[5x=25\]so rewriting either one or both of the equations as and equivalent equation allows you to arrange it so that one variable will add up to zero (cancel)