Technical Mathematics, Sixth Edition

Chapter 9. Systems of Linear Equations

OBJECTIVES When you have completed this chapter, you should be able to Find an approximate graphical solution to a system of two equations. Solve a system of two equations in two unknowns by the addition-subtraction method or by substitution. Solve a system of two equations by calculator. Solve a system of two equations having fractional coefficients or having the unknowns in the denominators. Solve a system of three equations by addition-subtraction, by substitution, or by calculator. Write a system of equations to describe an application problem and solve those equations.

Let us leave trigonometry for a while and return to our study of algebra. In an earlier chapter we learned how to solve a linear (first-degree) equation which has one unknown. Here we will show how to solve a set of two linear equations in which there are two unknowns.

Why? Because some problems in technology can only be described by two equations. For example, to find the two currents I₂ and I₂ in the circuit of Fig. 9-1, we must solve the two equations

We must find values for I₁ and I₂ that satisfy both equations at the same time.

Just as some applications need two equations for their description, others need three equations. We also study those in this chapter.

Here we will solve sets of equations using graphical or algebraic techniques, or both, and by calculator. In the ...