## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Section 7.2 - Systems of Linear Equations in Three Variables - Exercise Set - Page 831: 50

#### Answer

The statement makes sense.

#### Work Step by Step

Let us explain it with the help of an example. We use the elimination method to solve the two equations of the system except the equation in which one variable is missing. Then, solve the new equation and the initial equation with one missing variable to get the value of that missing variable in one equation. For instance, consider the system of equation as follows: $2x+6y+4z=16$ (I) $2x+2y=2$ (II) $6x+2y+4z=4$ (III) We eliminate z from equations (I) and (III) to get, \begin{align} & \text{ }2x+6y+4z=16 \\ & \underline{-6x-2y-4z=-4} \\ & -4x+4y\text{ }=12 \\ \end{align} (IV) Then, equations (II) and (IV) can be solved to get the value of one variable and then the system can be solved. Thus, the statement makes sense.

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