Graphical Method of Solving Equations

Core concept

Three possible outcomes exist: if the lines intersect at exactly one point, there is a unique solution (consistent, independent equations); if the lines are parallel and never meet, there is no solution (inconsistent equations); and if the lines coincide exactly (are the same line), there are infinitely many solutions (consistent, dependent equations). Recognising these three cases from the equations' coefficients, without even graphing, is a useful analytical skill developed alongside the graphical method.