how do you know when to add or subtract to eliminate

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You need to add or subtract to elimate terms when you have a literal equation, or an equation where there are two unknown variables. If you can elimate a term by adding or subtracting the equations, then it will make things much easier. Once you are left with one unknown variable, you can solve for it, then substitute it into one of the equations and find the other variable that you'd eliminated. Then, you can find the value for both variables! :)