5. Graphical Solution of non-Linear Systems

A non-linear graph is a curve. This section assumes you already know the formulas for straight lines, circles, parabolas, ellipses and hyperbolas. You can refresh your memory in the Plane Analytic Geometry chapter.

In this section, we see how to solve non-linear systems of equations (those involving curved lines), using a graph. Our answers (as `x`-`y` coordinates) will be approximate, and we can improve our answer by using a graphics calculator or a computer package.

Example

Solve the system of equations graphically:

3xy = 4

y = 6 − 2x2

Exercise 1

Solve graphically. Estimate your answer.

y = x2

xy = 4

Note: You can use the grapher on this page to get a better idea of what the graphs look like. You can also zoom in on the intersection points.

Exercise 2

Solve graphically. Estimate your answer:

y = 4xx2

y = 2 cos x