College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 5 - Systems of Equations and Inequalities - Exercise Set 5.2 - Page 537: 16


$\{ (2,2,2) \}$

Work Step by Step

Plan (see p.533): 1. Eliminate one variable and arrive at a system of two equations in two variables. 2. Solve the system of two equations in two variables. 3. Back-substitute the solutions of (2) to find the eliminated varable in (1) ------------ (1.) Perform elimination by addition method (eliminate $y$) by $Eq.2$ already is without x. $Eq.1-Eq.3 \Rightarrow$ $(1-0)x+(1-1)y+(0-1)z=4-0$ $\left[\begin{array}{ll} x+z=4 & I\\ x-z=0 & II \end{array}\right.$ , ({\it 2}.) ... $I+II$ eliminates $z$: $2x=4$ $z=2$ Back-substitute into $x+z=4$ $x+z=4$ $x=2$ (3.) Back-substitute into one of the initial equations: $y+z=4$ $y+2=4$ $y=2$ Solution set: : $\{ (2,2,2) \}$
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