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Graphing will never fail but it is much faster to look at what you have first to determine which method will be easier.
for example it the coefficient of one of the variables is 1 then you might want to use substitution. If the coefficients of one of the variables are already equal and opposite then use elimination. (add the equations you only have one variable to solve for)
my preference I look first.
the fourth method used to solve simultaneous equations is to use matrices.
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