Graphical Solving of the System of Two Equations with Two Variables

To solve graphically system of two equations with two variables, we need to draw graphs of the equations and find coordinates of points of intersections of these graphs.

Example. Solve the following system graphically: `{(x^2+y^2=25),(xy=12):}`.graphical solution of equations

Graph of the equation `x^2+y^2=25` is a circle with center at the origin and radius equal 5. Graph of the equation `xy=12` is a hyperbola `y=12/x`.

First we draw graphs of the equations and then find coordinates of points of intersection of circle and hyperbola: A(4;3), B(3;4), C(-4;-3), D(-3;-4).

Therefore, (4;3), (3;4), (-4;-3), (-3;-4) are solutions of the initial system.