substitution: solving one equation for x or y and substituting its value into the other equation to solve for one variable, then plugging this value into either equation to solve for the other variable.
elimination: manipulating the equations so that adding the first equation to the second will eliminate one of the variables so that the second variable can be solved for
graphing: graphing both equations and finding their point of intersection
Lines that do not intersect have no solution.
Lines that intersect once have one solution.
Lines that are the same have infinite solutions.