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okay so when were asked to solve a system of equations what are we really trying to do so in a case like this when we have it to such a system of two equations with two variables here or were really trying to find is we have two lines here we have two lines something like this not you know this is just random sketch of two lines were trying to find the intersection point of the two lines were trying to find the x and y coordinate of the intersection point and for example if one three dimensions we would and we have three variables three equations were trying to find the intersection point of three hyper planes in three dimensions three-dimensional Euclidean space i should note okay so there are two possible kind of things that could happen two main possible categories of things that could happen when we solve our system of equations one is that we have a consistent system which either means that we have one point of intersection here or we have essentially both lines being the sa