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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

Following are the original SNB files (.tex or .rap) used in making this chapter. For more information, go to SNB info.

SNB files

1. Simultaneous Linear Equations (SNB)

2. Graphs of Linear Functions (SNB)

3. Graphical Solution of Linear Systems (SNB)

4. Algebraic Solutions of Linear Systems (SNB)

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From the math blog...

5. Graphical Solution of non-Linear Systems

A non-linear graph is a curve.

In this section, we see how to solve non-linear systems of equations (those involving curved lines), using a graph. Our answer will probably be approximate, unless we use a graphics calculator or a computer package.

 

Example

Solve the system of equations graphically:

3x − y = 4

y = 6 − 2x²

Here is the LiveMath solution to this problem.

LIVEMath

And now for the "ordinary" answer:

Answer

Exercises

1 Solve graphically. Estimate your answer.

y = x²

xy = 4

Answer

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2 Solve graphically. Estimate your answer:

y = 4x - x²

y = 2 cos x

Answer