Instructions on How to use the Elimination Method










Are both equations in standard form?

 
 
 
 
NO

YES








Put them into standard form.


Are either the x's or y's opposites of each other?

 
 
 


NO

YES








Carefully select which variable you would like to eliminate. Multiply one or both equations by numbers that turn those variable terms into opposites


Add the two equations together.
Is one variable still left?
 YES

solve for that variable.

 




NO






 

Are you left with a true statement?

 

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!




NO


YES






This system has NO SOLUTIONS
It is called an inconsistent system

 

This system has INFINITELY MANY SOLUTIONS
It is called a consistent system.


CHECK YOUR WORK!
Substitute the ordered pair back into both equations to see if the values make both of them true.











 
 
 
 










 
 
 
 








