Chapter Contents

• Systems of Equations
• 1. Simultaneous Linear Equations
• 2. Graphs of Linear Functions
• 3. Graphical Solution of Linear Systems
• 4. Algebraic Solutions of Linear Systems
• 5. Graphical Solution of non-linear Systems
• 6. Algebraic Solution of non-Linear Systems
• Systems of Equations Problem Solver

• Comments, Questions?

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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 answer 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:

3x − y = 4

y = 6 − 2x²

Answer

Exercise 1

Solve graphically. Estimate your answer.

y = x²

xy = 4

Answer

Note: You can use the grapher on this page to see what the graphs look like. You can also zoom in on the intersection points.

Exercise 2

Solve graphically. Estimate your answer:

y = 4x − x²

y = 2 cos x

Answer