To solve an equation in one variable graphically, first manipulate the equation to put it in the form f(x) = 0, where x represents the variable present in the equation. Then use mathematical software, a graphing calculator or graph paper to plot the line y = f(x). The solution to f(x) = 0 is the point or points at which the line crosses the x-axis.
The graphical method of solving equations finds the point at which the lines y = f(x) and y = 0 intersect, which is the point at which f(x) = 0. If the line y = f(x) never crosses the x-axis, then the equation f(x) = 0 has no solution.
The limitation of graphical solutions is that only equations with one or two independent variables can be solved with this method. An equation with one variable leads to a two-dimensional plot; an equation with two variables leads to a three-dimensional plot. Plots with four or more dimensions are difficult to visualize accurately. It is also possible to solve sets of equations graphically by plotting each equation on the same plot. The point at which all of the lines (one variable) or planes (two variables) intersect, if there is one, is the solution to the set of equations.