Technical Mathematics, Sixth Edition

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:

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