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Technical Mathematics, Sixth Edition by Michael A. Calter Ph.D., Paul A. Calter

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9.1. Systems of Two Linear Equations

9.1.1. Linear Equations

We have previously defined a linear equation as one of first degree.

Example 1:

The equation

3x + 5 = 20

is a linear equation in one unknown. No term has a degree higher than 1. We learned how to solve these in Chap. 3.

Example 2:

The equation

y = 2x − 3

is a linear equation in two unknowns. If we graph this equation, we get a straight line, as shown in Fig. 9-2. Glance back at Chapter 5 if you've forgotten how to make such a graph.

Figure 9.2. FIGURE 9-2

9.1.2. Systems of Linear Equations

A set of two or more equations is called a system of equations. They are also called simultaneous equations.

Example 3:

  1. is a system of two linear equations in two unknowns.

  2. is a system of three linear equations in three unknowns.

  3. is also a system of three linear equations in three unknowns. Note that some variables may have coefficients of zero and not appear in every equation. This system can also be written

The systems of equations ...

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