Personally, I like gaussian reduction as a choice method, becausing my TI83 does it very quickly and accurately.
But for your methods, graphing on a graphing calc is fast. In school, often variables are assigned whole number values, which make elimination easy, but in real life (engineering), few answers are even rational numbers, much less whole numbers.
Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best? Why? What circumstances would cause you to use a different method?
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