Question 175598
there are actually more than 3. there is substitution, addition and subtraction commonly called elimination, graphing, matrix, cramers rule, and possibly more. The first two methods are commonly presented in Algebra I and Algebra II
texts. Solving systems using the last two methods is usually first explained
in Linear Algebra. Every method accomplishes the same purpose -- multiple unknowns are found from a 
system of simultaneous equations. Different methods are easier to use
depending on the problem. That’s why so many different methods are
shown.

strengths of graphing are you can see it visually and it can be a quick method
strengths of elimination is you generally dont have to manipulate the equations to much and its is pretty quick on most systems.
strengths of substitution- a little easier for some to grasp although it can end up being very tedious with some systems.
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matrix is one of my favorites because its quick(most of the time) and FUN
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hope that helps