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# CHAPTER 7

## 7.1 INTRODUCTION

The solution of a system of linear equations is an important topic for all engineering disciplines. In this chapter, the solution of 2 × 2 systems of equations will be carried out using four different methods: substitution method, graphical method, matrix algebra method, and Cramer's rule. It is assumed that the students are already familiar with the substitution and graphical methods from their high school algebra course, while the matrix algebra method and Cramer's rule are explained in detail. The objective of this chapter is to be able to solve the systems of equations encountered in beginning engineering courses such as physics, statics, dynamics, and DC circuit analysis. While the examples given are limited to 2 × 2 systems of equations, the matrix algebra approach is applicable to linear systems having any number of unknowns and is suitable for immediate implementation in MATLAB.

## 7.2 SOLUTION OF A TWO-LOOP CIRCUIT

Consider a two-loop resistive circuit with unknown currents I1 and I2 as shown in Fig. 7.1. Using a combination of Kirchhoff's voltage law (KVL) and Ohm's law, a system of two equations with two unknowns I1 and I2 can be obtained as

Figure 7.1 A two-loop resistive circuit.

Equations (7.1) and ...

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