Basic Technical Mathematics, 11th Edition

5.5 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

• Algebraic Method Using Addition or Subtraction • Solving a System Using Reduced Row Echelon Form

Many technical problems involve systems of linear equations with more than two unknowns. In this section, we solve systems with three unknowns, and in Chapter 16 we will show how systems with even more unknowns are solved.

Solving such systems is very similar to solving systems in two unknowns. In this section, we will show the algebraic method, and in the next section we will show how determinants are used. Graphical solutions are not used since a linear equation in three unknowns represents a plane in space. We will, however, briefly show graphical interpretations ...