Instructions on How to use the Elimination Method
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Are both equations in standard form?
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NO
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YES
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Put them into standard form.
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Are either the x's or y's opposites of each other?
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NO
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YES
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Carefully select which variable you would like to eliminate. Multiply one or both equations by numbers that turn those variable terms into opposites
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Add the two equations together.
Is one variable still left?
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YES
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solve for that variable.
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NO
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Are you left with a true statement?
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Substitute the value back into one of the original equations to find a value for the other variable.
Remember: we are looking for an ordered pair!
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NO
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YES
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This system has NO SOLUTIONS
It is called an inconsistent system
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This system has INFINITELY MANY SOLUTIONS
It is called a consistent system.
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CHECK YOUR WORK!
Substitute the ordered pair back into both equations to see if the values make both of them true.
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Elimination method
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